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  Subjects -> MATHEMATICS (Total: 894 journals)
    - APPLIED MATHEMATICS (74 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (662 journals)
    - MATHEMATICS (GENERAL) (42 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (662 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: 4)
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: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
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: 10)
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: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
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 Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
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: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
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: 7)
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: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
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: 4)
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: 4)
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: 20)
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  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
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: 9)
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: 3)
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: 1)
CHANCE     Hybrid Journal   (Followers: 5)
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: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
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: 4)
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: 6)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
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  
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)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     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: 3)
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)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  

        1 2 3 4 | Last

Journal Cover European Journal of Combinatorics
  [SJR: 1.233]   [H-I: 35]   [5 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 0195-6698 - ISSN (Online) 1095-9971
   Published by Elsevier Homepage  [3089 journals]
  • Polynomial expansion and sublinear separators
    • Abstract: Publication date: March 2018
      Source:European Journal of Combinatorics, Volume 69
      Author(s): Louis Esperet, Jean-Florent Raymond
      Let C be a class of graphs that is closed under taking subgraphs. We prove that if for some fixed 0 < δ ≤ 1 , every n -vertex graph of C has a balanced separator of order O ( n 1 − δ ) , then any depth- r minor (i.e. minor obtained by contracting disjoint subgraphs of radius at most r ) of a graph in C has average degree O ( ( r polylog r ) 1 ∕ δ ) . This confirms a conjecture of Dvořák and Norin.

      PubDate: 2017-11-19T01:38:06Z
       
  • On the complexity of H-coloring for special oriented trees
    • Abstract: Publication date: March 2018
      Source:European Journal of Combinatorics, Volume 69
      Author(s): Jakub Bulín
      For a fixed digraph H , the H -coloring problem is the problem of deciding whether a given input digraph G admits a homomorphism to H . The CSP dichotomy conjecture of Feder and Vardi is equivalent to proving that, for any H , the H -coloring problem is in P or NP-complete. We confirm this dichotomy for a certain class of oriented trees, which we call special trees (generalizing earlier results on special triads and polyads). Moreover, we prove that every tractable special oriented tree has bounded width, i.e., the corresponding H -coloring problem is solvable by local consistency checking. Our proof relies on recent algebraic tools, namely characterization of congruence meet-semidistributivity via pointing operations and absorption theory.

      PubDate: 2017-11-19T01:38:06Z
       
  • The odd–even invariant and Hamiltonian circuits in tope graphs
    • Abstract: Publication date: March 2018
      Source:European Journal of Combinatorics, Volume 69
      Author(s): Yvonne Kemper, Jim Lawrence
      Questions of the existence of Hamiltonian circuits in the tope graphs of central arrangements of hyperplanes are considered. Connections between the existence of Hamiltonian circuits in the arrangement and the odd–even invariant of the arrangement are described. Some new results concerning bounds on the odd–even invariant are obtained. All results can be formulated more generally for oriented matroids and are still valid in that setting.

      PubDate: 2017-11-19T01:38:06Z
       
  • Additive posets, CW-complexes, and graphs
    • Abstract: Publication date: March 2018
      Source:European Journal of Combinatorics, Volume 69
      Author(s): Vladimir Turaev
      We introduce and study additive posets. We show that the top homology group (with coefficients in Z ∕ 2 Z ) of a finite dimensional CW-complex carries a structure of an additive poset invariant under subdivisions. Applications to CW-complexes and graphs are discussed.

      PubDate: 2017-11-19T01:38:06Z
       
  • A new lower bound for van der Waerden numbers
    • Abstract: Publication date: March 2018
      Source:European Journal of Combinatorics, Volume 69
      Author(s): Thomas Blankenship, Jay Cummings, Vladislav Taranchuk
      In this paper we prove a new recurrence relation on the van der Waerden numbers, w ( r , k ) . In particular, if p is a prime and p ≤ k then w ( r , k ) > p ⋅ w r − r p , k − 1 . This recurrence gives the lower bound w ( r , p + 1 ) > p r − 1 2 p when r ≤ p , which generalizes Berlekamp’s theorem on 2-colorings, and gives the best known bound for a large interval of r . The recurrence can also be used to construct explicit valid colorings, and it improves known lower bounds on small van der Waerden numbers.

      PubDate: 2017-11-19T01:38:06Z
       
  • A fast scaling algorithm for the weighted triangle-free 2-matching problem
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): S. Artamonov, M. Babenko
      A perfect 2-matching in an undirected graph G = ( V , E ) is a function x : E → 0 , 1 , 2 such that for each node v ∈ V the sum of values x ( e ) on all edges e incident to v equals 2. If supp ( x ) = e ∈ E ∣ x ( e ) ≠ 0 contains no triangles then x is called triangle-free. Polyhedrally speaking, triangle-free 2-matchings are harder than 2-matchings, but easier than usual 1-matchings. Given edge costs c : E → R + , a natural combinatorial problem consists in finding a perfect triangle-free matching of minimum total cost. For this problem, Cornuéjols and Pulleyblank devised a combinatorial strongly-polynomial algorithm, which can be implemented to run in O ( V E log V ) time. (Here we write V , E to indicate their cardinalities V , E .) If edge costs are integers in range [ 0 , C ] then for both 1- and 2-matchings some faster scaling algorithms are known that find optimal solutions within O ( V α ( E , V ) log V E log ( V C ) ) and O ( V E log ( V C ) ) time, respectively, where α denotes the inverse Ackermann function. So far, no efficient cost-scaling algorithm is known for finding a minimum-cost perfect triangle-free2-matching. The present paper fills this gap by presenting such an algorithm with time complexity of O ( V E log V log ( V C ) ) .

      PubDate: 2017-11-19T01:38:06Z
       
  • 1-page and 2-page drawings with bounded number of crossings per edge
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Carla Binucci, Emilio Di Giacomo, Md. Iqbal Hossain, Giuseppe Liotta
      A drawing of a graph such that the vertices are drawn as points along a line and each edge is a circular arc in one of the two half-planes defined by this line is called a 2 -page drawing. If all edges are in the same half-plane, the drawing is called a 1 -page drawing. We want to compute 1 -page and 2 -page drawings of planar graphs such that the number of crossings per edge does not depend on the number of vertices. We show that for any constant k , there exist planar graphs that require more than k crossings per edge in both 1 -page and 2 -page drawings. We then prove that if the vertex degree is bounded by Δ , every planar 3-tree has a 2 -page drawing with a number of crossings per edge that only depends on Δ . Finally, we show a similar result for 1 -page drawings of partial 2 -trees.

      PubDate: 2017-11-19T01:38:06Z
       
  • 3-coloring triangle-free planar graphs with a precolored 9-cycle
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Ilkyoo Choi, Jan Ekstein, Přemysl Holub, Bernard Lidický
      Given a triangle-free planar graph G and a 9 -cycle C in G , we characterize situations where a 3 -coloring of C does not extend to a proper 3 -coloring of G . This extends previous results when C is a cycle of length at most 8 .

      PubDate: 2017-11-19T01:38:06Z
       
  • Contagious sets in dense graphs
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Daniel Freund, Matthias Poloczek, Daniel Reichman
      We study the activation process in undirected graphs known as bootstrap percolation: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it had at least  r active neighbors, for a threshold  r that is identical for all vertices. A contagious set is a vertex set whose activation results with the entire graph being active. Let  m ( G , r ) be the size of a smallest contagious set in a graph  G on  n vertices. We examine density conditions that ensure  m ( G , r ) = r for all  r , and first show a necessary and sufficient condition on the minimum degree. Moreover, we study the speed with which the activation spreads and provide tight upper bounds on the number of rounds it takes until all nodes are activated in such graphs. We also investigate what average degree asserts the existence of small contagious sets. For n ≥ k ≥ r , we denote by M ( n , k , r ) the maximum number of edges in an n -vertex graph G satisfying m ( G , r ) > k . We determine the precise value of M ( n , k , 2 ) and M ( n , k , k ) , assuming that  n is sufficiently large compared to  k .

      PubDate: 2017-11-19T01:38:06Z
       
  • On maximum common subgraph problems in series–parallel graphs
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Nils Kriege, Florian Kurpicz, Petra Mutzel
      The complexity of the maximum common connected subgraph problem in partial k -trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial 2 -trees. On the other hand, the problem is known to be NP-hard in vertex-labeled partial 11 -trees of bounded degree. We consider series–parallel graphs, i.e., partial 2 -trees. We show that the problem remains NP-hard in biconnected series–parallel graphs with all but one vertex of degree 3 or less. A positive complexity result is presented for a related problem of high practical relevance which asks for a maximum common connected subgraph that preserves blocks and bridges of the input graphs. We present a polynomial time algorithm for this problem in series–parallel graphs, which utilizes a combination of BC- and SP-tree data structures to decompose both graphs.

      PubDate: 2017-11-19T01:38:06Z
       
  • Computing heat kernel pagerank and a local clustering algorithm
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Fan Chung, Olivia Simpson
      Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating random walks of bounded length and runs in time O ( log ( ϵ − 1 ) log n ϵ 3 log log ( ϵ − 1 ) ) , assuming performing a random walk step and sampling from a distribution with bounded support take constant time. The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms. We present an efficient local clustering algorithm that finds cuts by performing a sweep over a heat kernel pagerank vector, using the heat kernel pagerank approximation algorithm as a subroutine. Specifically, we show that for a subset S of Cheeger ratio ϕ , many vertices in S may serve as seeds for a heat kernel pagerank vector which will find a cut of conductance O ( ϕ ) .

      PubDate: 2017-11-19T01:38:06Z
       
  • Decomposing the complete graph and the complete graph minus a 1-factor
           into copies of a graph G where G is the union of two disjoint cycles
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Saad I. El-Zanati, Uthoomporn Jongthawonwuth, Heather Jordon, Charles Vanden Eynden
      Let G of order n be the vertex-disjoint union of two cycles. It is known that there exists a G -decomposition of K v for all v ≡ 1 ( mod 2 n ) . If G is bipartite and x is a positive integer, it is also known that there exists a G -decomposition of K n x − I , where I is a 1-factor. If G is not bipartite, there exists a G -decomposition of K n if n is odd, and of K n − I , where I is a 1-factor, if n is even. We use novel extensions of the Bose construction for Steiner triple systems and some recent results on the Oberwolfach Problem to obtain a G -decomposition of K v for all v ≡ n ( mod 2 n ) when n is odd, unless G = C 4 ∪ C 5 and v = 9 . If G consists of two odd cycles and n ≡ 0 ( mod 4 ) , we also obtain a G -decomposition of K v − I , for all v ≡ 0 ( mod n ) , v ≠ 4 n .

      PubDate: 2017-11-19T01:38:06Z
       
  • Enumeration and maximum number of minimal connected vertex covers in
           graphs
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Petr A. Golovach, Pinar Heggernes, Dieter Kratsch
      Connected Vertex Cover is one of the classical problems of computer science, already mentioned in the monograph of Garey and Johnson (1979). Although the optimization and decision variants of finding connected vertex covers of minimum size or weight are well-studied, surprisingly there is no work on the enumeration or maximum number of minimal connected vertex covers of a graph. In this paper we show that the number of minimal connected vertex covers of a graph is at most 1 . 866 8 n , and these sets can be enumerated in time O ( 1 . 866 8 n ) . For graphs of chordality at most 5, we are able to give a better upper bound, and for chordal graphs and distance-hereditary graphs we are able to give tight bounds on the maximum number of minimal connected vertex covers.

      PubDate: 2017-11-19T01:38:06Z
       
  • A faster FPTAS for the Unbounded Knapsack Problem
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Klaus Jansen, Stefan E.J. Kraft
      The Unbounded Knapsack Problem (UKP) is a well-known variant of the famous 0–1 Knapsack Problem (0–1 KP). In contrast to 0–1 KP, an arbitrary number of copies of every item can be taken in UKP. Since UKP is NP-hard, fully polynomial time approximation schemes (FPTAS) are of great interest. Such algorithms find a solution arbitrarily close to the optimum OPT ( I ) , i.e., of value at least ( 1 − ε ) OPT ( I ) for ε > 0 , and have a running time polynomial in the input length and 1 ε . For over thirty years, the best FPTAS was due to Lawler with running time O ( n + 1 ε 3 ) and space complexity O ( n + 1 ε 2 ) , where n is the number of knapsack items. We present an improved FPTAS with running time O ( n + 1 ε 2 log 3 1 ε ) and space bound O ( n + 1 ε log 2 1 ε ) . This directly improves the running time of the fastest known approximation schemes for Bin Packing and Strip Packing, which have to approximately solve UKP instances as subproblems.

      PubDate: 2017-11-19T01:38:06Z
       
  • The k-leaf spanning tree problem admits a klam value of 39
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Meirav Zehavi
      The klam value of an algorithm that runs in time O ∗ ( f ( k ) ) is the maximal value k such that f ( k ) < 1 0 20 . Given a graph G and a parameter k , the k -Leaf Spanning Tree ( k -LST) problem asks if G contains a spanning tree with at least k leaves. This problem has been extensively studied over the past three decades. In 2000, Fellows et al. (2000) asked whether it admits a klam value of 50. A steady progress towards an affirmative answer continued until 5 years ago, when an algorithm of klam value 37 was discovered. Our contribution is twofold. First, we present an O ∗ ( 3 . 18 8 k ) -time parameterized algorithm for k -LST, which shows that the problem admits a klam value of 39. Second, we rely on an application of the bounded search trees technique where the correctness of rules crucially depends on the history of previously applied rules in a non-standard manner, encapsulated in a “dependency claim”. Similar claims may be used to capture the essence of other complex algorithms in a compact, useful manner.

      PubDate: 2017-11-19T01:38:06Z
       
  • Border correlations, lattices, and the subgraph component polynomial
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): F. Blanchet-Sadri, M. Cordier, R. Kirsch
      We consider the border sets of partial words and study the combinatorics of specific representations of them, called border correlations, which are binary vectors of same length indicating the borders. We characterize precisely which of these vectors are valid border correlations, and establish a one-to-one correspondence between the set of valid border correlations and the set of valid ternary period correlations of a given length, the latter being ternary vectors representing the strong and strictly weak period sets. It turns out that the sets of all border correlations of a given length form distributive lattices under suitably defined partial orderings. We also give connections between the ternary period correlation of a partial word and its refined border correlation which specifies the lengths of all the word’s bordered cyclic shifts’ minimal borders. Finally, we investigate the population size, that is, the number of partial words sharing a given (refined) border correlation, and obtain formulas to compute it. We do so using the subgraph component polynomial of an undirected graph, introduced recently by Tittmann et al. (2011), which counts the number of connected components in vertex induced subgraphs.

      PubDate: 2017-11-19T01:38:06Z
       
  • Computing primitively-rooted squares and runs in partial words
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): F. Blanchet-Sadri, J. Lazarow, J. Nikkel, J.D. Quigley, X. Zhang
      This paper deals with two types of repetitions in strings: squares, which consist of two adjacent occurrences of substrings, and runs, which are periodic substrings that cannot be extended further to the left or right while maintaining the period. We show how to compute all the primitively-rooted squares in a given partial word, which is a sequence that may have undefined positions, called holes or wildcards, that match any letter of the alphabet over which the sequence is defined. We also describe an algorithm for computing all primitively-rooted runs in a given partial word and extend previous analyses on the number of runs to partial words.

      PubDate: 2017-11-19T01:38:06Z
       
  • Longest common extension
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Béla Bollobás, Shoham Letzter
      Given a word w of length n and i , j ∈ [ n ] , the longest common extension is the longest substring starting at both i and j . In this note we estimate the average length of the longest common extension over all words w and all pairs ( i , j ) , as well as the typical maximum length of the longest common extension. We also consider a variant of this problem, due to Blanchet-Sadri and Lazarow, in which the word is allowed to contain ‘holes’, which are special symbols functioning as ‘jokers’, i.e. are considered to be equal to any character. In particular, we estimate the average longest common extension over all words w with a small number of holes, extending a result by Blanchet-Sadri, Harred and Lazarow, and prove a similar result for words with holes appearing randomly.

      PubDate: 2017-11-19T01:38:06Z
       
  • EERTREE: An efficient data structure for processing palindromes in strings
    • Abstract: Publication date: February 2018
      Source:European Journal of Combinatorics, Volume 68
      Author(s): Mikhail Rubinchik, Arseny M. Shur
      We propose a new linear-size data structure which provides a fast access to all palindromic substrings of a string or a set of strings. This structure inherits some ideas from the construction of both the suffix trie and suffix tree. Using this structure, we present simple and efficient solutions for a number of problems involving palindromes.

      PubDate: 2017-11-19T01:38:06Z
       
  • Multiple weak 2-linkage and its applications on integer flows of signed
           graphs
    • Abstract: Publication date: March 2018
      Source:European Journal of Combinatorics, Volume 69
      Author(s): You Lu, Rong Luo, Cun-Quan Zhang
      For two pairs of vertices x 1 , y 1 and x 2 , y 2 , Seymour and Thomassen independently presented a characterization of graphs containing no edge-disjoint ( x 1 , y 1 ) -path and ( x 2 , y 2 ) -path. In this paper we first generalize their result to k ≥ 2 pairs of vertices. Namely, for 2 k vertices x 1 , y 1 , x 2 , y 2 , … , x k , y k , we characterize the graphs without edge-disjoint ( x i , y i ) -path and ( x j , y j ) -path for any 1 ≤ i < j ≤ k . Then applying this generalization, we present a characterization of signed graphs in which there are no edge-disjoint unbalanced circuits. Finally with this characterization we further show that every flow-admissible signed graph without edge-disjoint unbalanced circuits admits a nowhere-zero 6 -flow and thus verify the well-known Bouchet’s 6 -flow conjecture for this family of signed graphs.

      PubDate: 2017-10-14T05:05:43Z
       
  • Best possible bounds concerning the set-wise union of families
    • Abstract: Publication date: March 2018
      Source:European Journal of Combinatorics, Volume 69
      Author(s): Peter Frankl
      For two families of sets F , G ⊂ 2 [ n ] we define their set-wise union, F ∨ G = { F ∪ G : F ∈ F , G ∈ G } and establish several – hopefully useful – inequalities concerning F ∨ G . Some applications are provided as well.

      PubDate: 2017-10-10T03:40:15Z
       
  • Fractional and circular separation dimension of graphs
    • Abstract: Publication date: March 2018
      Source:European Journal of Combinatorics, Volume 69
      Author(s): Sarah J. Loeb, Douglas B. West
      The separation dimension of a graph G , written π ( G ) , is the minimum number of linear orderings of V ( G ) such that every two nonincident edges are “separated” in some ordering, meaning that both endpoints of one edge appear before both endpoints of the other. We introduce the fractional separation dimension π f ( G ) , which is the minimum of a ∕ b such that some a linear orderings (repetition allowed) separate every two nonincident edges at least b times. In contrast to separation dimension, fractional separation dimension is bounded: always π f ( G ) ≤ 3 , with equality if and only if G contains K 4 . There is no stronger bound even for bipartite graphs, since π f ( K m , m ) = π f ( K m + 1 , m ) = 3 m m + 1 . We also compute π f ( G ) for cycles and some complete tripartite graphs. We show that π f ( G ) < 2 when G is a tree and present a sequence of trees on which the value tends to 4 ∕ 3 . Finally, we consider analogous problems for circular orderings, where pairs of nonincident edges are separated unless their endpoints alternate. Let π ∘ ( G ) be the number of circular orderings needed to separate all pairs and π f ∘ ( G ) be the fractional version. Among our results: (1) π ∘ ( G ) = 1 if and only G is outerplanar. (2) π ∘ ( G ) ≤ 2 when G is bipartite. (3) π ∘ ( K n ) ≥ log 2 log 3 ( n − 1 ) . (4) π f ∘
      PubDate: 2017-10-10T03:40:15Z
       
  • Small doubling in ordered nilpotent groups of class 2
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Gregory A. Freiman, Marcel Herzog, Patrizia Longobardi, Mercede Maj, Yonutz V. Stanchescu
      The aim of this paper is to present a complete description of the structure of finite subsets S of torsion-free nilpotent groups of class 2 satisfying S 2 = 3 S − 2 . In view of results in [12], this gives a complete description of the structure of finite subsets with the above property in any torsion-free nilpotent group.

      PubDate: 2017-10-10T03:40:15Z
       
  • Corrigendum to “On the limiting distribution of the metric dimension for
           random forests” [European J. Combin. 49 (2015) 68–89]
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Dieter Mitsche, Juanjo Rué


      PubDate: 2017-10-10T03:40:15Z
       
  • Hajós-like theorem for signed graphs
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Yingli Kang
      The paper designs five graph operations, and proves that every signed graph with chromatic number q , defined by Kang and Steffen (in press), can be obtained from copies of the all-positive complete graph ( K q , + ) by repeatedly applying these operations. This result gives a signed version of the Hajós theorem, emphasizing the role of all-positive complete graphs in the class of signed graphs, as in the class of unsigned graphs. Moreover, a similar result is established for the signed chromatic number defined by Máčajová, Raspaud and Škoviera.

      PubDate: 2017-09-25T12:48:29Z
       
  • Packing and covering odd cycles in cubic plane graphs with small faces
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Diego Nicodemos, Matěj Stehlík
      We show that any 3 -connected cubic plane graph on n vertices, with all faces of size at most 6 , can be made bipartite by deleting no more than ( p + 3 t ) n ∕ 5 edges, where p and t are the numbers of pentagonal and triangular faces, respectively. In particular, any such graph can be made bipartite by deleting at most 12 n ∕ 5 edges. This bound is tight, and we characterise the extremal graphs. We deduce tight lower bounds on the size of a maximum cut and a maximum independent set for this class of graphs. This extends and sharpens the results of Faria et al. (2012).

      PubDate: 2017-09-25T12:48:29Z
       
  • Uniqueness of the extreme cases in theorems of Drisko and
           Erdős–Ginzburg–Ziv
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Ron Aharoni, Dani Kotlar, Ran Ziv
      Drisko (1998) proved (essentially) that every family of 2 n − 1 matchings of size n in a bipartite graph possesses a partial rainbow matching of size n . In Barát et al. (2017) this was generalized as follows: Any ⌊ k + 2 k + 1 n ⌋ − ( k + 1 ) matchings of size n in a bipartite graph have a rainbow matching of size n − k . The paper has a twofold aim: (i) to extend these results to matchings of not necessarily equal cardinalities, and (ii) to prove a conjecture of Drisko, on the characterization of those families of 2 n − 2 matchings of size n in a bipartite graph that do not possess a rainbow matching of size n . Combining the latter with an idea of Alon (2011), we re-prove a characterization of the extreme case in a well-known theorem of Erdős–Ginzburg–Ziv in additive number theory.

      PubDate: 2017-09-25T12:48:29Z
       
  • Outside nested decompositions of skew diagrams and Schur function
           determinants
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Emma Yu Jin
      We describe the thickened strips and introduce the outside nested decompositions of any skew shape λ ∕ μ . For any such decomposition Φ = ( Θ 1 , Θ 2 , … , Θ g ) of the skew shape λ ∕ μ where Θ i is a thickened strip for every i , let r be the number of boxes that are contained in any two distinct thickened strips of Φ . Then we establish a determinantal formula of the function p 1 r ( X ) s λ ∕ μ ( X ) with the Schur functions of thickened strips as entries, where s λ ∕ μ ( X ) is the Schur function of the skew shape λ ∕ μ and p 1 r ( X ) is the power sum symmetric function indexed by the partition ( 1 r ) . This generalizes Hamel and Goulden’s theorem on the outside decompositions of the skew shape λ ∕ μ and our extension is motivated by the enumeration of m -strip tableaux, which was first counted by Baryshnikov and Romik via extending the transfer operator approach due to Elkies.

      PubDate: 2017-09-25T12:48:29Z
       
  • Stars versus stripes Ramsey numbers
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): G.R. Omidi, G. Raeisi, Z. Rahimi
      For given simple graphs G 1 , G 2 , … , G t , the Ramsey number R ( G 1 , G 2 , … , G t ) is the smallest positive integer n such that if the edges of the complete graph K n are partitioned into t disjoint color classes giving t graphs H 1 , H 2 , … , H t , then at least one H i has a subgraph isomorphic to G i . In this paper, for positive integers t 1 , t 2 , … , t s and n 1 , n 2 , … , n c the Ramsey number R ( S t 1 , S t 2 , … , S t s , n 1 K 2 , n 2 K 2 , … , n c K 2 ) is computed exactly, where n K 2 denotes a matching (stripe) of size n , i.e., n pairwise disjoint edges and S n is a star with n edges. This result generalizes and strengthens significantly a well-known result of Cockayne and Lorimer and also a known result of Gyárfás and Sárközy.

      PubDate: 2017-09-25T12:48:29Z
       
  • On sequences of polynomials arising from graph invariants
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): T. Kotek, J.A. Makowsky, E.V. Ravve
      Graph polynomials are deemed useful if they give rise to algebraic characterizations of various graph properties, and their evaluations encode many other graph invariants. Algebraic: The complete graphs K n and the complete bipartite graphs K n , n can be characterized as those graphs whose matching polynomials satisfy a certain recurrence relations and are related to the Hermite and Laguerre polynomials. An encoded graph invariant: The absolute value of the chromatic polynomial χ ( G , X ) of a graph G evaluated at − 1 counts the number of acyclic orientations of G . In this paper we prove a general theorem on graph families which are characterized by families of polynomials satisfying linear recurrence relations. This gives infinitely many instances similar to the characterization of K n , n . We also show where to use, instead of the Hermite and Laguerre polynomials, linear recurrence relations where the coefficients do not depend on n . Finally, we discuss the distinctive power of graph polynomials in specific form.

      PubDate: 2017-09-12T11:48:20Z
       
  • A note on the simplex-cosimplex problem
    • Abstract: Publication date: December 2017
      Source:European Journal of Combinatorics, Volume 66
      Author(s): Karim Adiprasito
      We construct, for every dimension d ≥ 3 , polytopal spheres S for which neither S nor its dual S ∗ contain 2-faces that are triangles. This answers the topological formulation of a problem of Kalai, Kleinschmidt and Meisinger.

      PubDate: 2017-09-06T10:39:44Z
       
  • Strong edge-colorings of sparse graphs with large maximum degree
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Ilkyoo Choi, Jaehoon Kim, Alexandr V. Kostochka, André Raspaud
      A strong k -edge-coloring of a graph G is a mapping from E ( G ) to { 1 , 2 , … , k } such that every two adjacent edges or two edges adjacent to the same edge receive distinct colors. The strong chromatic index χ s ′ ( G ) of a graph G is the smallest integer k such that G admits a strong k -edge-coloring. We give bounds on χ s ′ ( G ) in terms of the maximum degree Δ ( G ) of a graph G when G is sparse, namely, when G is 2 -degenerate or when the maximum average degree Mad ( G ) is small. We prove that the strong chromatic index of each 2 -degenerate graph G is at most 5 Δ ( G ) + 1 . Furthermore, we show that for a graph G , if Mad ( G ) < 8 ∕ 3 and Δ ( G ) ≥ 9 , then χ s ′ ( G ) ≤ 3 Δ ( G ) − 3 (the bound 3 Δ ( G ) − 3 is sharp) and if Mad ( G ) < 3 and Δ ( G ) ≥ 7 , then χ s ′ ( G ) ≤ 3 Δ ( G ) (the restriction Mad ( G ) < 3 is sharp).

      PubDate: 2017-08-31T10:06:55Z
       
  • Fourientation activities and the Tutte polynomial
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Spencer Backman, Sam Hopkins, Lorenzo Traldi
      A fourientation of a graph G is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. We may naturally view fourientations as a mixture of subgraphs and graph orientations where unoriented and bioriented edges play the role of absent and present subgraph edges, respectively. Building on work of Backman and Hopkins (forthcoming), we show that given a linear order and a reference orientation of the edge set, one can define activities for fourientations of G which allow for a new  12 variable expansion of the Tutte polynomial T G . Our formula specializes to both an orientation activities expansion of T G due to Las Vergnas (1984) and a generalized activities expansion of  T G due to Gordon and Traldi (1990).

      PubDate: 2017-08-31T10:06:55Z
       
  • Long minimal zero-sum sequences over a finite subset of Z
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Guixin Deng, Xiangneng Zeng
      Let G be an abelian group (written additively), X be a subset of G and S be a minimal zero-sum sequence over X . S is called unsplittable in X if there do not exist an element g in S and two elements x , y in X such that g = x + y and the new sequence S g − 1 x y is still a minimal zero-sum sequence. In this paper, we mainly investigate the case when G = Z and X = 〚 − m , n 〛 with m , n ∈ N . We obtain the structure of unsplittable minimal zero-sum sequences of length at least n + ⌊ m ∕ 2 ⌋ + 2 provided that n ≥ m 2 ∕ 2 − 1 and m ≥ 6 . As a corollary, the Davenport constant D ( 〚 − m , n 〛 ) is determined when n ≥ m 2 ∕ 2 − 1 . The Davenport constant D ( X ) for a general set X ⊂ Z is also discussed.

      PubDate: 2017-08-31T10:06:55Z
       
  • Decomposition of tournament limits
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Erik Thörnblad
      The theory of tournament limits and tournament kernels is developed by extending common notions for finite tournaments to this setting; in particular we study transitivity and irreducibility of limits and kernels. We prove that each tournament kernel and each tournament limit can be decomposed into a direct sum of irreducible components, with transitive components interlaced. We also show that this decomposition is essentially unique.

      PubDate: 2017-08-31T10:06:55Z
       
  • Reconstruction of infinite matroids from their 3-connected minors
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Nathan Bowler, Johannes Carmesin, Luke Postle
      We show that any infinite matroid can be reconstructed from the torsos of a tree-decomposition over its 2-separations, together with local information at the ends of the tree. We show that if the matroid is tame then this local information is simply a choice of whether circuits are permitted to use that end. The same is true if each torso is planar, with all gluing elements on a common face.

      PubDate: 2017-08-31T10:06:55Z
       
  • Gorenstein simplices and the associated finite abelian groups
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Akiyoshi Tsuchiya
      It is known that a lattice simplex of dimension d corresponds a finite abelian subgroup of ( R ∕ Z ) d + 1 . Conversely, given a finite abelian subgroup of ( R ∕ Z ) d + 1 such that the sum of all entries of each element is an integer, we can obtain a lattice simplex of dimension d . In this paper, we discuss a characterization of Gorenstein simplices in terms of the associated finite abelian groups. In particular, we present complete characterizations of Gorenstein simplices whose normalized volume equals p , p 2 and p q , where p and q are prime numbers with p ≠ q . Moreover, we compute the volume of the associated dual reflexive simplices of the Gorenstein simplices.

      PubDate: 2017-08-31T10:06:55Z
       
  • Modular flip-graphs of one-holed surfaces
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Hugo Parlier, Lionel Pournin
      We study flip-graphs of triangulations on topological surfaces where distance is measured by counting the number of necessary flip operations between two triangulations. We focus on surfaces of positive genus g with a single boundary curve and n marked points on this curve and consider triangulations up to homeomorphism with the marked points as their vertices. Our results are bounds on the maximal distance between two triangulations. Our lower bounds assert that these distances grow at least like 5 n ∕ 2 for all g ≥ 1 . Our upper bounds grow at most like [ 4 − 1 ∕ ( 4 g ) ] n for g ≥ 2 , and at most like 23 n ∕ 8 for the bordered torus.

      PubDate: 2017-08-31T10:06:55Z
       
  • Approximating set multi-covers
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Márton Naszódi, Alexandr Polyanskii
      Johnson and Lovász and Stein proved independently that any hypergraph satisfies τ ≤ ( 1 + ln Δ ) τ ∗ , where τ is the transversal number, τ ∗ is its fractional version, and Δ denotes the maximum degree. We prove τ f ≤ 3 . 153 τ ∗ max { ln Δ , f } for the f -fold transversal number τ f . Similarly to Johnson, Lovász and Stein, we also show that this bound can be achieved non-probabilistically, using a greedy algorithm. As a combinatorial application, we prove an estimate on how fast τ f ∕ f converges to τ ∗ . As a geometric application, we obtain an upper bound on the minimal density of an f -fold covering of the d -dimensional Euclidean space by translates of any convex body.

      PubDate: 2017-08-31T10:06:55Z
       
  • The k-strong induced arboricity of a graph
    • Abstract: Publication date: January 2018
      Source:European Journal of Combinatorics, Volume 67
      Author(s): Maria Axenovich, Daniel Gonçalves, Jonathan Rollin, Torsten Ueckerdt
      The induced arboricity of a graph G is the smallest number of induced forests covering the edges of G . This is a well-defined parameter bounded from above by the number of edges of G when each forest in a cover consists of exactly one edge. Not all edges of a graph necessarily belong to induced forests with larger components. For k ⩾ 1 , we call an edge k -valid if it is contained in an induced tree on k edges. The k -strong induced arboricity of G , denoted by f k ( G ) , is the smallest number of induced forests with components of sizes at least k that cover all k -valid edges in G . This parameter is highly non-monotone. However, we prove that for any proper minor-closed graph class C , and more generally for any class of bounded expansion, and any k ⩾ 1 , the maximum value of f k ( G ) for G ∈ C is bounded from above by a constant depending only on C and k . This implies that the adjacent closed vertex-distinguishing number of graphs from a class of bounded expansion is bounded by a constant depending only on the class. We further prove that f 2 ( G ) ⩽ 3 t + 1 3 for any graph G of tree-width  t and that f k ( G ) ⩽ ( 2 k ) d for any graph of tree-depth d . In addition, we prove that f 2 ( G ) ⩽ 310 when G is planar.

      PubDate: 2017-07-28T08:19:36Z
       
 
 
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