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  Subjects -> MATHEMATICS (Total: 912 journals)
    - APPLIED MATHEMATICS (76 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (678 journals)
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MATHEMATICS (678 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 25)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 6)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 11)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 9)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 7)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 3)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 6)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 7)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 10)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)

        1 2 3 4 | Last

Journal Cover Discrete Mathematics
  [SJR: 1]   [H-I: 55]   [8 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0012-365X
   Published by Elsevier Homepage  [3120 journals]
  • A simple characterization of special matchings in lower Bruhat intervals
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Fabrizio Caselli, Mario Marietti
      We give a simple characterization of special matchings in lower Bruhat intervals (that is, intervals starting from the identity element) of a Coxeter group. As a byproduct, we obtain some results on the action of special matchings.

      PubDate: 2018-01-09T18:37:20Z
       
  • Null decomposition of trees
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Daniel A. Jaume, Gonzalo Molina
      Let T be a tree. We show that the null space of the adjacency matrix of T has relevant information about the structure of T . We introduce the Null Decomposition of trees, which is a decomposition into two different types of trees: N-trees and S-trees. N-trees are the trees that have a unique maximum (perfect) matching. S-trees are the trees with a unique maximum independent set. We obtain formulas for the independence number and the matching number of a tree using this decomposition. We also show how the number of maximum matchings and the number of maximum independent sets in a tree are related to its null decomposition.

      PubDate: 2018-01-09T18:37:20Z
       
  • An update on non-Hamiltonian 54-tough maximal planar graphs
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Adam Kabela
      Studying the shortness of longest cycles in maximal planar graphs, we improve the upper bound on the shortness exponent of the class of 5 4 -tough maximal planar graphs presented by Harant and Owens (1995). In addition, we present two generalizations of a similar result of Tkáč who considered 1 -tough maximal planar graphs (Tkáč, 1996); we remark that one of these generalizations gives a tight upper bound. We fix a problematic argument used in both mentioned papers.

      PubDate: 2017-12-26T18:12:52Z
       
  • Planar graphs without 3-cycles adjacent to cycles of length 3 or 5 are
           (3,1)-colorable
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Zhengke Miao, Yingqian Wang, Chuanni Zhang, Huajun Zhang
      Given a nonnegative integer d and a positive integer k , a graph G is said to be ( k , d ) -colorable if the vertices of G can be colored with k colors such that every vertex has at most d neighbors receiving the same color as itself. Let ℱ be the family of planar graphs without 3 -cycles adjacent to cycles of length 3 or 5. This paper proves that everyone in ℱ is ( 3 , 1 ) -colorable. This is the best possible in the sense that there are members in ℱ which are not ( 3 , 0 ) -colorable.

      PubDate: 2017-12-26T18:12:52Z
       
  • Choosability with union separation
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Mohit Kumbhat, Kevin Moss, Derrick Stolee
      List coloring generalizes graph coloring by requiring the color of a vertex to be selected from a list of colors specific to that vertex. One refinement of list coloring, called choosability with separation, requires that the intersection of adjacent lists is sufficiently small. We introduce a new refinement, called choosability with union separation, where we require that the union of adjacent lists is sufficiently large. For t ≥ k , a ( k , t ) -list assignment is a list assignment L where L ( v ) ≥ k for all vertices v and L ( u ) ∪ L ( v ) ≥ t for all edges u v . A graph is ( k , t ) -choosable if there is a proper coloring for every ( k , t ) -list assignment. We explore this concept through examples of graphs that are not ( k , t ) -choosable, demonstrating sparsity conditions that imply a graph is ( k , t ) -choosable, and proving that all planar graphs are ( 3 , 11 ) -choosable and ( 4 , 9 ) -choosable.

      PubDate: 2017-12-26T18:12:52Z
       
  • The parity Hamiltonian cycle problem
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Hiroshi Nishiyama, Yusuke Kobayashi, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita
      Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every vertex an odd number of times, where we remark that the walk may use an edge more than once. First, we give a complete characterization of the graphs which have PHCs, and give a linear time algorithm to find a PHC, in which every edge appears at most four times, in fact. In contrast, we show that finding a PHC is NP -hard if a closed walk is allowed to use each edge at most z times for each z = 1 , 2 , 3 ( PHC z for short), even when a given graph is two-edge-connected. We then further investigate the PHC 3 problem, and show that the problem is in P when an input graph is four-edge-connected. Finally, we are concerned with three (or two)-edge-connected graphs, and show that the PHC 3 problem is in P for any C ≥ 5 -free or P 6 -free graphs. Note that the Hamiltonian cycle problem is known to be NP -hard for those graph classes.

      PubDate: 2017-12-26T18:12:52Z
       
  • Some bounds on the number of colors in interval and cyclic interval edge
           colorings of graphs
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Carl Johan Casselgren, Hrant H. Khachatrian, Petros A. Petrosyan
      An interval t -coloring of a multigraph G is a proper edge coloring with colors 1 , … , t such that the colors of the edges incident with every vertex of G are colored by consecutive colors. A cyclic interval t -coloring of a multigraph G is a proper edge coloring with colors 1 , … , t such that the colors of the edges incident with every vertex of G are colored by consecutive colors, under the condition that color 1 is considered as consecutive to color t . Denote by w ( G ) ( w c ( G ) ) and W ( G ) ( W c ( G ) ) the minimum and maximum number of colors in a (cyclic) interval coloring of a multigraph G , respectively. We present some new sharp bounds on w ( G ) and W ( G ) for multigraphs G satisfying various conditions. In particular, we show that if G is a 2 -connected multigraph with an interval coloring, then W ( G ) ≤ 1 + V ( G ) 2 ( Δ ( G ) − 1 ) . We also give several results towards the general conjecture that W c ( G ) ≤ V ( G ) for any triangle-free graph G with a cyclic interval coloring; we establish that approximate versions of this conjecture hold for several families of graphs, and we prove that the conjecture is true for graphs with maximum degree at most 4 .

      PubDate: 2017-12-26T18:12:52Z
       
  • On the existence of 3- and 4-kernels in digraphs
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Sebastián González Hermosillo de la Maza, César Hernández-Cruz
      Let D = ( V ( D ) , A ( D ) ) be a digraph. A subset S ⊆ V ( D ) is k -independent if the distance between every pair of vertices of S is at least k , and it is ℓ -absorbent if for every vertex u in V ( D ) ∖ S there exists v ∈ S such that the distance from u to v is less than or equal to ℓ . A k -kernel is a k -independent and ( k − 1 ) -absorbent set. A kernel is simply a 2 -kernel. A classical result due to Duchet states that if every directed cycle in a digraph D has at least one symmetric arc, then D has a kernel. We propose a conjecture generalizing this result for k -kernels and prove it true for k = 3 and k = 4 .

      PubDate: 2017-12-26T18:12:52Z
       
  • A note on panchromatic colorings
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Danila Cherkashin
      This paper studies the quantity p ( n , r ) , that is the minimal number of edges of an n -uniform hypergraph without panchromatic coloring (it means that every edge meets every color) in r colors. If r ≤ c n ln n then all bounds have a type A 1 ( n , ln n , r ) ( r r − 1 ) n ≤ p ( n , r ) ≤ A 2 ( n , r , ln r ) ( r r − 1 ) n , where A 1 , A 2 are some algebraic fractions. The main result is a new lower bound on p ( n , r ) when r is at least c n ; we improve an upper bound on p ( n , r ) if n = o ( r 3 ∕ 2 ) . Also we show that p ( n , r ) has upper and lower bounds depending only on n ∕ r when the ratio n ∕ r is small, which cannot be reached by the previous probabilistic machinery. Finally we construct an explicit example of a hypergraph without panchromatic coloring and with ( r r − 1 + o ( 1 ) ) n edges for r = o ( n ln n ) .

      PubDate: 2017-12-26T18:12:52Z
       
  • Proper colouring Painter–Builder game
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Małgorzata Bednarska-Bzdęga, Michael Krivelevich, Viola Mészáros, Clément Requilé
      We consider the following two-player game, parametrised by positive integers n and k . The game is played between Painter and Builder, alternately taking turns, with Painter moving first. The game starts with the empty graph on n vertices. In each round Painter colours a vertex of her choice by one of the k colours and Builder adds an edge between two previously unconnected vertices. Both players must adhere to the restriction that the game graph is properly k -coloured. The game ends if either all n vertices have been coloured, or Painter has no legal move. In the former case, Painter wins the game; in the latter one, Builder is the winner. We prove that the minimal number of colours k = k ( n ) allowing Painter’s win is of logarithmic order in the number of vertices n . Biased versions of the game are also considered.

      PubDate: 2017-12-26T18:12:52Z
       
  • Query complexity of mastermind variants
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Aaron Berger, Christopher Chute, Matthew Stone
      We study variants of Mastermind, a popular board game in which the objective is sequence reconstruction. In this two-player game, the so-called codemaker constructs a hidden sequence H = ( h 1 , h 2 , … , h n ) of colors selected from an alphabet A = { 1 , 2 , … , k } (i.e., h i ∈ A for all i ∈ { 1 , 2 , … , n } ). The game then proceeds in turns, each of which consists of two parts: in turn t , the second player (the codebreaker) first submits a query sequence Q t = ( q 1 , q 2 , … , q n ) with q i ∈ A for all i , and second receives feedback Δ ( Q t , H ) , where Δ is some agreed-upon function of distance between two sequences with n components. The game terminates when the codebreaker has determined the value of H , and the codebreaker seeks to end the game in as few turns as possible. Throughout we let f ( n , k ) denote the smallest integer such that the codebreaker can determine any H in f ( n , k ) turns. We prove three main results: First, when H is known to be a permutation of { 1 , 2 , … , n } , we prove that f ( n , n ) ≥ n − log log n for all sufficiently large n . Second, we show that Knuth’s Minimax algorithm identifies any H in at most n k queries. Third, when feedback is not received until all queries have been submitted, we show that f ( n , k ) = Ω ( n log k ) .

      PubDate: 2017-12-26T18:12:52Z
       
  • On the spanning connectivity of the generalized Petersen graphs P(n,3)
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Jeng-Jung Wang, Lih-Hsing Hsu
      In this paper, we employed lattice model to describe the three internally vertex-disjoint paths that span the vertex set of the generalized Petersen graph P ( n , 3 ) . We showed that the P ( n , 3 ) is 3-spanning connected for odd n . Based on the lattice model, five amalgamated and one extension mechanisms are introduced to recursively establish the 3-spanning connectivity of the P ( n , 3 ) . In each amalgamated mechanism, a particular lattice trail was amalgamated with the lattice trails that was dismembered, transferred, or extended from parts of the lattice trails for P ( n − 6 , 3 ) , where a lattice tail is a trail in the lattice model that represents a path in P ( n , 3 ) .

      PubDate: 2017-12-26T18:12:52Z
       
  • Inverse relations in Shapiro’s open questions
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Ik-Pyo Kim, Michael J. Tsatsomeros
      As an inverse relation, involution with an invariant sequence plays a key role in combinatorics and features prominently in some of Shapiro’s open questions (Shapiro, 2001). In this paper, invariant sequences are used to provide answers to some of these questions about the Fibonacci matrix and Riordan involutions.

      PubDate: 2017-12-26T18:12:52Z
       
  • Orthogonally Resolvable Matching Designs
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): P. Danziger, S. Park
      An orthogonally resolvable matching design OMD ( n , k ) is a partition of the edges of the complete graph K n into matchings of size k , called blocks, such that the blocks can be resolved in two different ways. Such a design can be represented as a square array whose cells are either empty or contain a matching of size k , where every vertex appears exactly once in each row and column. In this paper we show that an OMD ( n , k ) exists if and only if n ≡ 0 ( mod 2 k ) except when k = 1 and n = 4 or 6 .

      PubDate: 2017-12-26T18:12:52Z
       
  • A problem on partial sums in abelian groups
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): S. Costa, F. Morini, A. Pasotti, M.A. Pellegrini
      In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group that naturally arises investigating simple Heffter systems. Then we show its connection with related open problems and we present some results about the validity of these conjectures.

      PubDate: 2017-12-26T18:12:52Z
       
  • The list chromatic index of simple graphs whose odd cycles intersect in at
           most one edge
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Jessica McDonald, Gregory J. Puleo
      We study the class of simple graphs G ∗ for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in G ∗ and prove that every G ∈ G ∗ satisfies the list-edge-coloring conjecture. When Δ ( G ) ≥ 4 , we in fact prove a stronger result about kernel-perfect orientations in L ( G ) which implies that G is ( m Δ ( G ) : m ) -edge-choosable and Δ ( G ) -edge-paintable for every m ≥ 1 .

      PubDate: 2017-12-26T18:12:52Z
       
  • A sharp lower bound on Steiner Wiener index for trees with given diameter
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Lu Lu, Qiongxiang Huang, Jiangxia Hou, Xun Chen
      Let G be a connected graph with vertex set V ( G ) and edge set E ( G ) . For a subset S of V ( G ) , the Steiner distance d ( S ) of S is the minimum size of a connected subgraph whose vertex set contains S . For an integer k with 2 ≤ k ≤ n − 1 , the Steiner k -Wiener index SW k ( G ) is ∑ S ⊆ V ( G ) , S = k d ( S ) . In this paper, we introduce some transformations for trees that do not increase their Steiner k -Wiener index for 2 ≤ k ≤ n − 1 . Using these transformations, we get a sharp lower bound on Steiner k -Wiener index for trees with given diameter, and obtain the corresponding extremal graph as well.

      PubDate: 2017-12-26T18:12:52Z
       
  • The smallest surface that contains all signed graphs on K4,n
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Shengxiang Lv, Zihan Yuan
      Finding the smallest number of crosscaps that suffice to orientation-embed every edge signature of the complete bipartite graph K m , n is an open problem. In this paper that number for the complete bipartite graph K 4 , n , n ≥ 4 , is determined by using diamond products of signed graphs. The number is 2 ⌊ n − 1 2 ⌋ + 1 , which is attained by K 4 , n with exactly 1 negative edge, except that when n = 4 , the number is 4, which is attained by K 4 , 4 with exactly 4 independent negative edges.

      PubDate: 2017-12-26T18:12:52Z
       
  • d-matching in 3-uniform hypergraphs
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Yi Zhang, Mei Lu
      A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. A d -matching in a 3-uniform hypergraph H is a matching of size d . Let V 1 , V 2 be a partition of n vertices such that V 1 = 2 d − 1 and V 2 = n − 2 d + 1 . Denote by E 3 ( 2 d − 1 , n − 2 d + 1 ) the 3-uniform hypergraph with vertex set V 1 ∪ V 2 consisting of all those edges which contain at least two vertices of V 1 . Let H be a 3-uniform hypergraph of order n ≥ 9 d 2 such that d e g ( u ) + d e g ( v ) > 2 [ n − 1 2 − n − d 2 ] for any two adjacent vertices u , v ∈ V ( H ) . In this paper, we prove H contains a d -matching if and only if H is not a subgraph of E 3 ( 2 d − 1 , n − 2 d + 1 ) .

      PubDate: 2017-12-26T18:12:52Z
       
  • On the weight distributions of a class of cyclic codes
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Hongwei Liu, Xiaoqiang Wang, Dabin Zheng
      Let m and k be two positive integers such that v 2 ( m ) = v 2 ( k ) , where v 2 ( ⋅ ) denotes the 2-valuation function, and let α be a primitive element of F p 2 m . Let C be a cyclic code over F p with a parity-check polynomial h 1 ( x ) h 2 ( x ) h 3 ( x ) ∈ F p 2 m [ x ] , where h 1 ( x ) , h 2 ( x ) and h 3 ( x ) are the minimal polynomials of α − p k + 1 2 , − α − p k + 1 2 and α − p m + 1 2 over F p respectively. In this paper, we determine the weight distribution and the complete weight distribution of the code C .

      PubDate: 2017-12-26T18:12:52Z
       
  • On the excess of vertex-transitive graphs of given degree and girth
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Slobodan Filipovski, Robert Jajcay
      We consider a restriction of the well-known Cage Problem to the class of vertex-transitive graphs, and consider the problem of finding the smallest vertex-transitive k -regular graphs of girth g . Counting cycles to obtain necessary arithmetic conditions on the parameters ( k , g ) , we extend previous results of Biggs, and prove that, for any given excess e and any given degree k ≥ 4 , the asymptotic density of the set of girths g for which there exists a vertex-transitive ( k , g ) -cage with excess not exceeding e is 0.

      PubDate: 2017-12-26T18:12:52Z
       
  • Graph coloring and Graham’s greatest common divisor problem
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Bartłomiej Bosek, Michał Dębski, Jarosław Grytczuk, Joanna Sokół, Małgorzata Śleszyńska-Nowak, Wiktor Żelazny
      In this paper we introduce and study two graph coloring problems and relate them to some deep number-theoretic problems. For a fixed positive integer k consider a graph B k whose vertex set is the set of all positive integers with two vertices a , b joined by an edge whenever the two numbers a ∕ gcd ( a , b ) and b ∕ gcd ( a , b ) are both at most k . We conjecture that the chromatic number of every such graph B k is equal to k . This would generalize the greatest common divisor problem of Graham from 1970; in graph-theoretic terminology it states that the clique number of B k is equal to k . Our conjecture is connected to integer lattice tilings and partial Latin squares completions.

      PubDate: 2017-12-26T18:12:52Z
       
  • A note on Bartholdi zeta function and graph invariants based on resistance
           distance
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Deqiong Li, Yaoping Hou
      Let G be a finite connected graph. In this note, we show that the complexity of G can be obtained from the partial derivatives at ( 1 − 1 t , t ) of a determinant in terms of the Bartholdi zeta function of G . Moreover, the second order partial derivatives at ( 1 − 1 t , t ) of this determinant can all be expressed as the linear combination of the Kirchhoff index, the additive degree-Kirchhoff index, and the multiplicative degree-Kirchhoff index of the graph G .

      PubDate: 2017-12-26T18:12:52Z
       
  • Minimizing the number of independent sets in triangle-free regular graphs
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Jonathan Cutler, A.J. Radcliffe
      Recently, Davies, Jenssen, Perkins, and Roberts gave a very nice proof of the result (due, in various parts, to Kahn, Galvin–Tetali, and Zhao) that the independence polynomial of a d -regular graph is maximized by disjoint copies of K d , d . Their proof uses linear programming bounds on the distribution of a cleverly chosen random variable. In this paper, we use this method to give lower bounds on the independence polynomial of regular graphs. We also give a new bound on the number of independent sets in triangle-free cubic graphs.

      PubDate: 2017-12-26T18:12:52Z
       
  • Global forcing number for maximal matchings
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Damir Vukičević, Shuang Zhao, Jelena Sedlar, Shou-Jun Xu, Tomislav Došlić
      Let M ( G ) denote the set of all maximal matchings in a simple graph G , and f : M ( G ) → { 0 , 1 } E ( G ) be the characteristic function of maximal matchings of G . Any set S ⊆ E ( G ) such that f S is an injection is called a global forcing set for maximal matchings in G , and the cardinality of smallest such S is called the global forcing number for maximal matchings of G . In this paper we establish sharp lower and upper bounds on this quantity and prove explicit formulas for certain classes of graphs. At the end, we also state some open problems and discuss some further developments.

      PubDate: 2017-12-26T18:12:52Z
       
  • Multi-set neighbor distinguishing 3-edge coloring
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): Bojan Vučković
      Let G be a graph without isolated edges, and let c : E ( G ) → { 1 , … , k } be a coloring of the edges, where adjacent edges may be colored the same. The color code of a vertex v is the ordered k -tuple ( a 1 , a 2 , … , a k ) , where a i is the number of edges incident with v that are colored i . If every two adjacent vertices of G have different color codes, such a coloring is called multi-set neighbor distinguishing. In this paper, we prove that three colors are sufficient to produce a multi-set neighbor distinguishing edge coloring for every graph without isolated edges.

      PubDate: 2017-12-26T18:12:52Z
       
  • Heights of minor 5-stars in 3-polytopes with minimum degree 5 and no
           vertices of degree 6 and 7
    • Abstract: Publication date: March 2018
      Source:Discrete Mathematics, Volume 341, Issue 3
      Author(s): O.V. Borodin, A.O. Ivanova, O.N. Kazak, E.I. Vasil’eva
      Given a 3-polytope P , by h ( P ) we denote the minimum of the maximum degrees (height) of the neighborhoods of 5-vertices (minor 5-stars) in P . In 1940, H. Lebesgue gave an approximate description of the neighborhoods of 5-vertices in the class P 5 of 3-polytopes with minimum degree 5. In 1996, S. Jendrol’ and T. Madaras showed that if a polytope P in P 5 is allowed to have a 5-vertex adjacent to four 5-vertices (called a minor ( 5 , 5 , 5 , 5 , ∞ ) -star), then h ( P ) can be arbitrarily large. For each P ∗ in P 5 with neither vertices of degree 6 or 7 nor minor ( 5 , 5 , 5 , 5 , ∞ ) -star, it follows from Lebesgue’s theorem that h ( P ∗ ) ≤ 23 . We prove that every such polytope P ∗ satisfies h ( P ∗ ) ≤ 14 , which bound is sharp. Moreover, if 6-vertices are allowed but 7-vertices forbidden, or vice versa, then the height of minor 5-stars in P 5 under the absence of minor ( 5 , 5 , 5 , 5 , ∞ ) -stars can reach 15 or 17, respectively.

      PubDate: 2017-12-26T18:12:52Z
       
  • Equation-regular sets and the Fox–Kleitman conjecture
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): S.D. Adhikari, L. Boza, S. Eliahou, M.P. Revuelta, M.I. Sanz
      Given k ≥ 1 , the Fox–Kleitman conjecture from 2006 states that there exists a nonzero integer b such that the 2 k -variable linear Diophantine equation ∑ i = 1 k ( x i − y i ) = b is ( 2 k − 1 ) -regular. This is best possible, since Fox and Kleitman showed that for all b ≥ 1 , this equation is not 2 k -regular. While the conjecture has recently been settled for all k ≥ 2 , here we focus on the case k = 3 and determine the degree of regularity of the corresponding equation for all b ≥ 1 . In particular, this independently confirms the conjecture for k = 3 . We also briefly discuss the case k = 4 .

      PubDate: 2017-12-26T18:12:52Z
       
  • Ideal ramp schemes and related combinatorial objects
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Douglas R. Stinson
      In 1996, Jackson and Martin (Jackson and Martin, 1996) proved that a strong ideal ramp scheme is equivalent to an orthogonal array. However, there was no good characterization of ideal ramp schemes that are not strong. Here we show the equivalence of ideal ramp schemes to a new variant of orthogonal arrays that we term augmented orthogonal arrays. We give some constructions for these new kinds of arrays, and, as a consequence, we also provide parameter situations where ideal ramp schemes exist but strong ideal ramp schemes do not exist.

      PubDate: 2017-12-26T18:12:52Z
       
  • Asymptotically good quasi-cyclic codes of fractional index
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Jiafu Mi, Xiwang Cao
      Generalizing the quasi-cyclic codes of index 1 1 3 introduced by Fan et al., we study a more general class of quasi-cyclic codes of fractional index generated by pairs of polynomials. The parity check polynomial and encoder of these codes are obtained. The asymptotic behaviours of the rates and relative distances of this class of codes are studied by using a probabilistic method. We prove that, for any positive real number δ such that the asymptotic GV-bound at k + l 2 δ is greater than 1 2 , the relative distance of the code is convergent to δ , while the rate is convergent to 1 k + l . As a result, quasi-cyclic codes of fractional index are asymptotically good.

      PubDate: 2017-12-26T18:12:52Z
       
  • Fair and internally fair (holey) hamiltonian decompositions of
           K(n0,…,np−1;λ1,λ2)
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Aras Erzurumluoğlu, C.A. Rodger
      Let G = K ( n 0 , … , n p − 1 ; λ 1 , λ 2 ) be the graph with p parts V 0 , V 1 , … , V p − 1 of n 0 , … , n p − 1 vertices, respectively, where there are λ 1 edges between each pair of vertices from the same part and λ 2 edges between each pair of vertices from distinct parts. A holey hamilton cycle of deficiency V i of G is a hamilton cycle of G − V i for some i satisfying 0 ≤ i ≤ p − 1 . A holey hamiltonian decomposition is a set of holey hamilton cycles whose edges partition E ( G ) . Representing each (holey) hamilton cycle as a color class in an edge-coloring, a (holey) hamiltonian decomposition of G is said to be fair if between each pair of (not necessarily distinct) parts the (permitted) color classes have size within one of each other—so the edges between a pair of parts are shared “evenly” among the (permitted) color classes. Similarly, a (holey) factorization of G is said to be internally fair if within each color class the edges between vertices of distinct parts are shared evenly among all pairs of distinct parts (for which that color class is permitted), and if within each color class the edges joining vertices from the same part are shared evenly among all parts (for which that color class is permitted). In this paper the existence of fair hamiltonian and fair holey hamiltonian decompositions of G are each settled except in a few cases. Simultaneously we settle the existence of internally fair and internally fair holey hamiltonian decompositions of G in a slightly more general setting.

      PubDate: 2017-12-26T18:12:52Z
       
  • On self-dual constacyclic codes of length ps over Fpm+uFpm
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Hai Q. Dinh, Yun Fan, Hualu Liu, Xiusheng Liu, Songsak Sriboonchitta
      The aim of this paper is to establish all self-dual λ -constacyclic codes of length p s over the finite commutative chain ring R = F p m + u F p m , where p is a prime and u 2 = 0 . If λ = α + u β for nonzero elements α , β of F p m , the ideal 〈 u 〉 is the unique self-dual ( α + u β ) -constacyclic codes. If λ = γ for some nonzero element γ of F p m , we consider two cases of γ . When γ = γ − 1 , i.e., γ = 1 or − 1 , we first obtain the dual of every cyclic code, a formula for the number of those cyclic codes and identify all self-dual cyclic codes. Then we use the ring isomorphism φ to carry over the results about cyclic accordingly to negacyclic codes. When γ ≠ γ − 1 , it is shown that 〈 u 〉 is the unique self-dual γ -constacyclic code. Among other results, the number of each type of self-dual constacyclic code is obtained.

      PubDate: 2017-12-26T18:12:52Z
       
  • Combinatorial and probabilistic formulae for divided symmetrization
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): F. Petrov
      Divided symmetrization of a function f ( x 1 , … , x n ) is symmetrization of the ratio D S G ( f ) = f ( x 1 , … , x n ) ∏ ( x i − x j ) , where the product is taken over the set of edges of some graph G . We concentrate on the case when G is a tree and f is a polynomial of degree n − 1 , in this case D S G ( f ) is a constant function. We give a combinatorial interpretation of the divided symmetrization of monomials for general trees and probabilistic game interpretation for a tree which is a path. In particular, this implies a result by Postnikov originally proved by computing volumes of special polytopes, and suggests its generalization.

      PubDate: 2017-12-26T18:12:52Z
       
  • Lonesum decomposable matrices
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Ken Kamano
      A lonesum matrix is a ( 0 , 1 ) -matrix that is uniquely determined by its row and column sum vectors. In this paper, we introduce lonesum decomposable matrices and study their properties. We provide a necessary and sufficient condition for a matrix A to be lonesum decomposable, and give a generating function for the number D k ( m , n ) of m × n lonesum decomposable matrices of order k . Moreover, by using this generating function we prove some congruences for D k ( m , n ) modulo a prime.

      PubDate: 2017-12-26T18:12:52Z
       
  • Two-weight and three-weight codes from trace codes over Fp+uFp+vFp+uvFp
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Yan Liu, Minjia Shi, Patrick Solé
      We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the non-chain ring F p + u F p + v F p + u v F p , where u 2 = 0 , v 2 = 0 , u v = v u . These codes are defined as trace codes. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. With a linear Gray map, we obtain a class of abelian three-weight codes and two-weight codes over F p . In particular, the two-weight codes we describe are shown to be optimal by application of the Griesmer bound. We also discuss their dual Lee distance. Finally, an application to secret sharing schemes is given.

      PubDate: 2017-12-26T18:12:52Z
       
  • A generalized Goulden–Jackson cluster method and lattice path
           enumeration
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Yan Zhuang
      The Goulden–Jackson cluster method is a powerful tool for obtaining generating functions counting words in a free monoid by occurrences of a set of subwords. We introduce a generalization of the cluster method for monoid networks, which generalize the combinatorial framework of free monoids. As a sample application of the generalized cluster method, we compute bivariate and multivariate generating functions counting Motzkin paths – both with height bounded and unbounded – by statistics corresponding to the number of occurrences of various subwords, yielding both closed-form and continued fraction formulas.

      PubDate: 2017-12-26T18:12:52Z
       
  • The D-optimal saturated designs of order 22
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Vasilis Chasiotis, Stratis Kounias, Nikos Farmakis
      This paper attempts to prove the D-optimality of the saturated designs X ∗ and X ∗ ∗ of order 22, already existing in the current literature. The corresponding non-equivalent information matrices M ∗ =(X ∗ ) T X ∗ and M ∗ ∗ =(X ∗ ∗ ) T X ∗ ∗ have the maximum determinant. Within the application of a specific procedure, all symmetric and positive definite matrices M of order 22 with determinant the square of an integer and ≥ det(M ∗ ) are constructed. This procedure has indicated that there are 26 such non-equivalent matrices M, for 24 of which the non-existence of designs X such that X T X =M is proved. The remaining two matrices M are the information matrices M ∗ and M ∗ ∗ .

      PubDate: 2017-12-26T18:12:52Z
       
  • Between Shi and Ish
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Rui Duarte, António Guedes de Oliveira
      We introduce a new family of hyperplane arrangements in dimension n ≥ 3 that includes both the Shi arrangement and the Ish arrangement. We prove that all the members of a given subfamily have the same number of regions – the connected components of the complement of the union of the hyperplanes – which can be bijectively labeled with the Pak–Stanley labeling. In addition, we show that, in the cases of the Shi and the Ish arrangements, the number of labels with reverse centers of a given length is equal, and conjecture that the same happens with all of the members of the family.

      PubDate: 2017-12-26T18:12:52Z
       
  • A property on reinforcing edge-disjoint spanning hypertrees in uniform
           hypergraphs
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Xiaofeng Gu, Hong-Jian Lai
      Suppose that H is a simple uniform hypergraph satisfying E ( H ) = k ( V ( H ) − 1 ) . A k -partition π = ( X 1 , X 2 , … , X k ) of E ( H ) such that X i = V ( H ) − 1 for 1 ≤ i ≤ k is a uniform k -partition. Let P k ( H ) be the collection of all uniform k -partitions of E ( H ) and define ε ( π ) = ∑ i = 1 k c ( H ( X i ) ) − k , where c ( H ) denotes the number of maximal partition-connected sub-hypergraphs of H . Let ε ( H ) = min π ∈ P k ( H ) ε ( π ) . Then ε ( H ) ≥ 0 with equality holds if and only if H is a union of k edge-disjoint spanning hypertrees. The parameter ε ( H ) is used to measure how close H is being from a union of k edge-disjoint spanning hypertrees. We prove that if H is a simple uniform hypergraph with E ( H ) = k ( V ( H ) − 1 ) and ε ( H ) > 0 , then there exist e ∈ E ( H ) and e ′ ∈ E ( H c ) such that ε ( H −...
      PubDate: 2017-12-26T18:12:52Z
       
  • Transversals in completely reducible multiary quasigroups and in multiary
           quasigroups of order 4
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): A.A. Taranenko
      An n -ary quasigroup f of order q is an n -ary operation over a set of cardinality q such that the Cayley table of the operation is an n -dimensional latin hypercube of order q . A transversal in a quasigroup f (or in the corresponding latin hypercube) is a collection of q ( n + 1 ) -tuples from the Cayley table of f , each pair of tuples differing at each position. The problem of transversals in latin hypercubes was posed by Wanless in 2011. An n -ary quasigroup f is called reducible if it can be obtained as a composition of two quasigroups whose arity is at least 2, and it is completely reducible if it can be decomposed into binary quasigroups. In this paper we investigate transversals in reducible quasigroups and in quasigroups of order 4. We find a lower bound on the number of transversals for a vast class of completely reducible quasigroups. Next we prove that, except for the iterated group Z 4 of even arity, every n -ary quasigroup of order 4 has a transversal. Also we obtain a lower bound on the number of transversals in quasigroups of order 4 and odd arity and count transversals in the iterated group Z 4 of odd arity and in the iterated group Z 2 2 . All results of this paper can be regarded as those concerning latin hypercubes.

      PubDate: 2017-12-26T18:12:52Z
       
  • On a class of quaternary complex Hadamard matrices
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Kai Fender, Hadi Kharaghani, Sho Suda
      We introduce a class of regular unit Hadamard matrices whose entries consist of two complex numbers and their conjugates for a total of four complex numbers. We then show that these matrices are contained in the Bose–Mesner algebra of an association scheme arising from skew Paley matrices.

      PubDate: 2017-12-26T18:12:52Z
       
  • Enumerating cycles in the graph of overlapping permutations
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): John Asplund, N. Bradley Fox
      The graph of overlapping permutations is a directed graph that is an analogue to the De Bruijn graph. It consists of vertices that are permutations of length n and edges that are permutations of length n + 1 in which an edge a 1 ⋯ a n + 1 would connect the standardization of a 1 ⋯ a n to the standardization of a 2 ⋯ a n + 1 . We examine properties of this graph to determine where directed cycles can exist, to count the number of directed 2 -cycles within the graph, and to enumerate the vertices that are contained within closed walks and directed cycles of more general lengths.

      PubDate: 2017-12-26T18:12:52Z
       
  • Game of cops and robbers in oriented quotients of the integer grid
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Seyyed Aliasghar Hosseini, Bojan Mohar
      The integer grid Z □ Z has four typical orientations of its edges which make it a vertex-transitive digraph. In this paper we analyze the game of Cops and Robbers on arbitrary finite quotients of these directed grids.

      PubDate: 2017-12-26T18:12:52Z
       
  • Improved FPT algorithms for weighted independent set in bull-free graphs
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Henri Perret du Cray, Ignasi Sau
      Very recently, Thomassé et al. (2017) have given an FPT algorithm for Weighted Independent Set in bull-free graphs parameterized by the weight of the solution, running in time 2 O ( k 5 ) ⋅ n 9 . In this article we improve this running time to 2 O ( k 2 ) ⋅ n 7 . As a byproduct, we also improve the previous Turing-kernel for this problem from O ( k 5 ) to O ( k 2 ) . Furthermore, for the subclass of bull-free graphs without holes of length at most 2 p − 1 for p ≥ 3 , we speed up the running time to 2 O ( k ⋅ k 1 p − 1 ) ⋅ n 7 . As p grows, this running time is asymptotically tight in terms of k , since we prove that for each integer p ≥ 3 , Weighted Independent Set cannot be solved in time 2 o ( k ) ⋅ n O ( 1 ) in the class of { bull , C 4 , … , C 2 p − 1 } -free graphs unless the ETH fails.

      PubDate: 2017-12-26T18:12:52Z
       
  • Structure and algorithms for (cap, even hole)-free graphs
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Kathie Cameron, Murilo V.G. da Silva, Shenwei Huang, Kristina Vušković
      A graph is even-hole-free if it has no induced even cycles of length 4 or more. A cap is a cycle of length at least 5 with exactly one chord and that chord creates a triangle with the cycle. In this paper, we consider (cap, even hole)-free graphs, and more generally, (cap, 4-hole)-free odd-signable graphs. We give an explicit construction of these graphs. We prove that every such graph G has a vertex of degree at most 3 2 ω ( G ) − 1 , and hence χ ( G ) ≤ 3 2 ω ( G ) , where ω ( G ) denotes the size of a largest clique in G and χ ( G ) denotes the chromatic number of G . We give an O ( n m ) algorithm for q -coloring these graphs for fixed q and an O ( n m ) algorithm for maximum weight stable set, where n is the number of vertices and m is the number of edges of the input graph. We also give a polynomial-time algorithm for minimum coloring. Our algorithms are based on our results that triangle-free odd-signable graphs have treewidth at most 5 and thus have clique-width at most 48, and that (cap, 4-hole)-free odd-signable graphs G without clique cutsets have treewidth at most 6 ω ( G ) − 1 and clique-width at most 48.

      PubDate: 2017-12-26T18:12:52Z
       
  • Packing chromatic number of cubic graphs
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): József Balogh, Alexandr Kostochka, Xujun Liu
      A packing k -coloring of a graph G is a partition of V ( G ) into sets V 1 , … , V k such that for each 1 ≤ i ≤ k the distance between any two distinct x , y ∈ V i is at least i + 1 . The packing chromatic number, χ p ( G ) , of a graph G is the minimum k such that G has a packing k -coloring. Sloper showed that there are 4 -regular graphs with arbitrarily large packing chromatic number. The question whether the packing chromatic number of subcubic graphs is bounded appears in several papers. We answer this question in the negative. Moreover, we show that for every fixed k and g ≥ 2 k + 2 , almost every n -vertex cubic graph of girth at least g has the packing chromatic number greater than k .

      PubDate: 2017-12-26T18:12:52Z
       
  • Degree sequence conditions for maximally edge-connected and
           super-edge-connected digraphs depending on the clique number
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Sebastian Milz, Lutz Volkmann
      Let D be a finite and simple digraph with vertex set V ( D ) . For a vertex v ∈ V ( D ) , the degree d ( v ) of v is defined as the minimum value of its out-degree d + ( v ) and its in-degree d − ( v ) . If D is a graph or a digraph with minimum degree δ and edge-connectivity λ , then λ ≤ δ . A graph or a digraph is maximally edge-connected if λ = δ . A graph or a digraph is called super-edge-connected if every minimum edge-cut consists of edges adjacent to or from a vertex of minimum degree. In this note we present degree sequence conditions for maximally edge-connected and super-edge-connected digraphs depending on the clique number of the underlying graph.

      PubDate: 2017-12-26T18:12:52Z
       
  • Turán numbers of vertex-disjoint cliques in r-partite graphs
    • Abstract: Publication date: February 2018
      Source:Discrete Mathematics, Volume 341, Issue 2
      Author(s): Jessica De Silva, Kristin Heysse, Adam Kapilow, Anna Schenfisch, Michael Young
      For two graphs G and H , the Turán number ex ( G , H ) is the maximum number of edges in a subgraph of G that contains no copy of H . Chen, Li, and Tu determined the Turán numbers ex ( K m , n , k K 2 ) for all k ≥ 1 Chen et al. (2009). In this paper we will determine the Turán numbers ex ( K a 1 , … , a r , k K r ) for all r ≥ 3 and k ≥ 1 .

      PubDate: 2017-12-26T18:12:52Z
       
 
 
JournalTOCs
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