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  Subjects -> MATHEMATICS (Total: 886 journals)
    - APPLIED MATHEMATICS (72 journals)
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    - MATHEMATICS (656 journals)
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MATHEMATICS (656 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
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: 8)
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: 22)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 8)
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: 1)
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: 8)
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: 9)
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: 6)
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: 19)
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: 2)
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: 1)
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: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 8)
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  
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: 5)
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: 2)
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)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
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  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Electronic Notes in Discrete Mathematics
  [SJR: 0.32]   [H-I: 15]   [2 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 1571-0653
   Published by Elsevier Homepage  [3043 journals]
  • Fair representation in dimatroids
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Ron Aharoni, Eli Berger, Dani Kotlar, Ran Ziv
      For a simplicial complex C denote by β ( C ) the minimal number of edges from C needed to cover the ground set. If C is a matroid then for every partition A 1 , … , A m of the ground set there exists a set S ∈ C meeting each A i in at least A i β ( C ) elements. We conjecture a slightly weaker statement for the intersection of two matroids: if D = P ∩ Q , where P , Q are matroids on the same ground set V, and β ( P ) , β ( Q ) ≤ k , then for every partition A 1 , … , A m of the ground set there exists a set S ∈ D meeting each A i in at least 1 k A i − 1 elements. We prove that when m = 2 there is a set meeting each A i in at least ( 1 k − 1 V ) A i − 1 elements.

      PubDate: 2017-08-31T22:46:30Z
       
  • Quasirandomness in hypergraphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Elad Aigner-Horev, David Conlon, Hiệp Hàn, Yury Person, Mathias Schacht
      A graph G is called quasirandom if it possesses typical properties of the corresponding random graph G ( n , p ) with the same edge density as G. A well-known theorem of Chung, Graham and Wilson states that, in fact, many such ‘typical’ properties are asymptotically equivalent and, thus, a graph G possessing one property immediately satisfies the others. In recent years, more quasirandom graph properties have been found and extensions to hypergraphs have been explored. For the latter, however, there exist several distinct notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. The purpose of this paper is to give short purely combinatorial proofs of most of Towsner's results.

      PubDate: 2017-08-31T22:46:30Z
       
  • Linear quasi-randomness of subsets of abelian groups and hypergraphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Elad Aigner-Horev, Hiệp Hàn
      We establish an equivalence between the two seemingly distant notions of quasi-randomness: small linear bias of subsets of abelian groups and uniform edge distribution for uniform hypergraphs. For a subset A ⊂ G of an abelian group G consider the k-uniform Cayley (sum) hypergraph H ( k ) ( A ) . The vertex set of H ( k ) A is G and the edges are k-element sets { x 1 , … , x k } ∈ ( G k ) with x 1 + … + x k ∈ A . For d ∈ ( 0 , 1 ) we show that sets A ⊂ G of density d + o ( 1 ) have all non-trivial Fourier coefficients of order o ( G ) if and only if e ( U ) = d ( U k ) + o ( G k ) for all U ⊂ V ( H ( k ) ( A ) ) . This connects the work of Chung and Graham on quasi-random subsets of the integers and that of Conlon-Hàn-Person-Schacht on weak/linear quasi-random hypergraphs. Further, it extends the work of Chung and Graham who established the corresponding result for k = 2 and G = Z n .

      PubDate: 2017-08-31T22:46:30Z
       
  • Colorings of b-simple hypergraphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Margarita Akhmejanova, Dmitry Shabanov
      The paper deals with an extremal problem concerning colorings of hypergraphs with bounded edge degrees. Consider the family of b-simple hypergraphs, in which any two edges do not share more than b common vertices. We prove that for n ≥ n 0 ( b ) , any n-uniform b-simple hypergraph with the maximum edge degree at most c n r n − b is r-colorable, where c > 0 is an absolute constant.

      PubDate: 2017-08-31T22:46:30Z
       
  • Packing degenerate graphs greedily
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Peter Allen, Julia Böttcher, Jan Hladký, Diana Piguet
      We prove that if G is a family of graphs with at most n vertices each, with constant degeneracy, with maximum degree at most O ( n / log ⁡ n ) , and with total number of edges at most ( 1 − o ( 1 ) ) ( n 2 ) , then G packs into the complete graph K n .

      PubDate: 2017-08-31T22:46:30Z
       
  • Completing graphs to metric spaces
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Andrés Aranda, David Bradley-Williams, Eng Keat Hng, Jan Hubička, Miltiadis Karamanlis, Michael Kompatscher, Matěj Konečný, Micheal Pawliuk
      We prove that certain classes of metrically homogeneous graphs omitting triangles of odd short perimeter as well as triangles of long perimeter have the extension property for partial automorphisms and we describe their Ramsey expansions.

      PubDate: 2017-08-31T22:46:30Z
       
  • Enumerating Polyominoes with Fixed Perimeter Defect
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Andrei Asinowski, Gill Barequet, Yufei Zheng
      A polyomino is an edge-connected set of cells on Z 2 . To-date, no formulae enumerating polyominoes by area (number of cells) or perimeter (number of empty cells neighboring the polyomino) are known. We present a few formulae enumerating polyominoes with a fixed deviation from the maximum possible perimeter.

      PubDate: 2017-08-31T22:46:30Z
       
  • On Induced Colourful Paths in Triangle-free Graphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Jasine Babu, Manu Basavaraju, L. Sunil Chandran, Mathew C. Francis
      Given a graph G = ( V , E ) whose vertices have been properly coloured, we say that a path in G is colourful if no two vertices in the path have the same colour. It is a corollary of the Gallai-Roy Theorem that every properly coloured graph contains a colourful path on χ ( G ) vertices. We explore a conjecture that states that every properly coloured triangle-free graph G contains an induced colourful path on χ ( G ) vertices and prove its correctness when the girth of G is at least χ ( G ) . Recent work on this conjecture by Gyárfás and Sárközy, and Scott and Seymour has shown the existence of a function f such that if χ ( G ) ≥ f ( k ) , then an induced colourful path on k vertices is guaranteed to exist in any properly coloured triangle-free graph G.

      PubDate: 2017-08-31T22:46:30Z
       
  • Induced Ramsey-type results and binary predicates for point sets
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Martin Balko, Jan Kynčl, Stefan Langerman, Alexander Pilz
      Let A and B be two finite sets of points in the plane in general position (neither of these sets contains three collinear points). We say that A lies deep below B if every point from A lies below every line determined by two points from B and every point from B lies above every line determined by two points from A. A point set P is decomposable if either P = 1 or there is a partition P 1 ∪ P 2 of P into nonempty and decomposable sets such that P 1 is to the left of P 2 and P 1 is deep below P 2. Extending a result of Nešetřil and Valtr, we show that for every decomposable point set Q and a positive integer k there is a finite set P of points in the plane in general position that satisfies the following Ramsey-type statement. For any partition C 1 ∪ ⋯ ∪ C k of the pairs of points from P (that is, of the edges of the complete graph on P), there is a subset Q ′ of P with the same triple-orientations as Q such that all pairs of points from Q ′ are in the same part C i . We then use this result to show that for every k there is a point set P such that no function Γ that maps ordered pairs of distinct points from P to a set of size k can satisfy the following property: if Γ attains the same values on two ordered triples of points from P, then these triples have the same orientation. Intuitively, this implies that there cannot be such a function that is defined locally and determines the orientation of point triples.

      PubDate: 2017-08-31T22:46:30Z
       
  • Equiangular lines and subspaces in Euclidean spaces
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Igor Balla, Felix Dräxler, Peter Keevash, Benny Sudakov
      A family of lines through the origin in a Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R n was studied extensively for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, we prove that for every fixed angle θ and n sufficiently large, there are at most 2 n − 2 lines in R n with common angle θ. Moreover, this is achievable only for θ = arccos ⁡ 1 3 . We also study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum size of an equiangular set of k-dimensional subspaces in R n , obtaining bounds which extend and improve a result of Blokhuis.

      PubDate: 2017-08-31T22:46:30Z
       
  • Resilience for the Littlewood-Offord Problem
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Afonso S. Bandeira, Asaf Ferber, Matthew Kwan
      Consider the sum X ( ξ ) = ∑ i = 1 n a i ξ i , where a = ( a i ) i = 1 n is a sequence of non-zero reals and ξ = ( ξ i ) i = 1 n is a sequence of i.i.d. Rademacher random variables (that is, Pr [ ξ i = 1 ] = Pr [ ξ i = − 1 ] = 1 / 2 ). The classical Littlewood-Offord problem asks for the best possible upper bound on the concentration probabilities Pr [ X = x ] . We study a resilience version of the Littlewood-Offord problem: how many of the ξ i is an adversary typically allowed to change without being able to force concentration on a particular value' We solve this problem asymptotically, demonstrating an interesting connection to the notion of an additive basis from additive combinatorics. We also present several interesting open problems.

      PubDate: 2017-08-31T22:46:30Z
       
  • Loose Hamiltonian cycles forced by large (k−2)-degree - sharp
           version
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): J. de O. Bastos, G.O. Mota, M. Schacht, J. Schnitzer, F. Schulenburg
      We prove for all k ≥ 4 and 1 ≤ ℓ < k / 2 the sharp minimum ( k − 2 )-degree bound for a k-uniform hypergraph H on n vertices to contain a Hamiltonian ℓ-cycle if k − ℓ divides n and n is sufficiently large. This extends a result of Han and Zhao for 3-uniform hypergraphs.

      PubDate: 2017-08-31T22:46:30Z
       
  • Complementary cycles in regular bipartite tournaments: a proof of
           Manoussakis, Song and Zhang Conjecture
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Stéphane Bessy, Jocelyn Thiebaut
      Let D be a k-regular bipartite tournament. We show that, for every even p with 4 ≤ p ≤ V ( D ) − 4 , D has a cycle C of size p such that D \ C is Hamiltonian unless D is isomorphic to a special digraph, F 4 k . This result proves a conjecture of Manoussakis, Song and Zhang.

      PubDate: 2017-08-31T22:46:30Z
       
  • Staircases, dominoes, and the growth rate of 1324-avoiders
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): David Bevan, Robert Brignall, Andrew Elvey Price, Jay Pantone
      We establish a lower bound of 10.271 for the growth rate of the permutations avoiding 1324, and an upper bound of 13.5. This is done by first finding the precise growth rate of a subclass whose enumeration is related to West-2-stack-sortable permutations, and then combining copies of this subclass in particular ways.

      PubDate: 2017-08-31T22:46:30Z
       
  • Some properties of the skeleton of the pyramidal tours polytope
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Vladimir Bondarenko, Andrei Nikolaev
      We consider the skeleton of the pyramidal tours polytope PYR(n) that is defined as the convex hull of characteristic vectors of all pyramidal tours in the complete graph K n . We describe necessary and sufficient condition for the adjacency of vertices of PYR(n) polytope. Based on that, we establish that the diameter of PYR(n) skeleton equals 2, and the asymptotically exact estimate of PYR(n) skeleton's clique number is Θ ( n 2 ) . This value characterizes the time complexity in a broad class of algorithms based on linear comparisons.

      PubDate: 2017-08-31T22:46:30Z
       
  • The Interactive Sum Choice Number of Graphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Marthe Bonamy, Kitty Meeks
      We introduce a variant of the well-studied sum choice number of graphs, which we call the interactive sum choice number. In this variant, we request colours to be added to the vertices' colour-lists one at a time, and so we are able to make use of information about the colours assigned so far to determine our future choices. The interactive sum choice number cannot exceed the sum choice number and we conjecture that, except in the case of complete graphs, the interactive sum choice number is always strictly smaller than the sum choice number. In this paper we provide evidence in support of this conjecture, demonstrating that it holds for a number of graph classes, and indeed that in many cases the difference between the two quantities grows as a linear function of the number of vertices.

      PubDate: 2017-08-31T22:46:30Z
       
  • Decomposition of 8-regular graphs into paths of length 4
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Fábio Botler, Alexandre Talon
      A P ℓ -decomposition of a graph G is a set of edge-disjoint copies of P ℓ in G that cover the edge set of G, where P ℓ is the path with ℓ edges. Kouider and Lonc [M. Kouider, Z. Lonc, Path decompositions and perfect path double covers, Australas. J. Combin. 19 (1999) 261–274] conjectured that any 2ℓ-regular graph G admits a P ℓ -decomposition D where every vertex of G is the end-vertex of exactly two paths of D. In this paper we verify Kouider and Lonc's Conjecture for paths of length 4.

      PubDate: 2017-08-31T22:46:30Z
       
  • Embedding spanning bounded degree subgraphs in randomly perturbed graphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Julia Böttcher, Richard Montgomery, Olaf Parczyk, Yury Person
      We study the model of randomly perturbed dense graphs, which is the union of any graph G α with minimum degree αn and the binomial random graph G ( n , p ) . For p = ω ( n − 2 / ( Δ + 1 ) ) , we show that G α ∪ G ( n , p ) contains any single spanning graph with maximum degree Δ. As in previous results concerning this model, the bound for p we use is lower by a log-term in comparison to the bound known to be needed to find the same subgraph in G ( n , p ) alone.

      PubDate: 2017-08-31T22:46:30Z
       
  • K4-expansions have the edge-Erdős-Pósa property
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Henning Bruhn, Matthias Heinlein
      A family F of graphs has the edge-Erdős-Pósa property if there is a function f : N → N such that for every k ∈ N and every graph G, the following holds: either G contains k edge-disjoint subgraphs contained in F or there is an edge set Y of size at most f(k) such that G − Y does not contain any subgraph in F . We prove that the family of graphs that have K 4 as a minor has the edge-Erdős-Pósa property.

      PubDate: 2017-08-31T22:46:30Z
       
  • Directed Ramsey number for trees
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Matija Bucić, Shoham Letzter, Benny Sudakov
      Given an oriented graph H, the k-colour oriented Ramsey number of H, denoted by r → ( H , k ) , is the least integer n, for which every k-edge-coloured tournament on n vertices contains a monochromatic copy of H. We show that r → ( T , k ) ≤ c k T k for any oriented tree T, which, in general, is tight up to a constant factor. We also obtain a stronger bound, when H is an arbitrarily oriented path.

      PubDate: 2017-08-31T22:46:30Z
       
  • Monochromatic paths in random tournaments
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Matija Bucić, Shoham Letzter, Benny Sudakov
      We prove that, with high probability, any 2-edge colouring of a random tournament on n vertices contains a monochromatic path of length Ω ( n / log ⁡ n ) . This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.

      PubDate: 2017-08-31T22:46:30Z
       
  • Almost partitioning 2-edge-colourings of 3-uniform hypergraphs with two
           monochromatic tight cycles
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Sebastián Bustamante, Hiệp Hàn, Maya Stein
      We show that any 2-colouring of the 3-uniform complete hypergraph K n ( 3 ) on n vertices contains two disjoint monochromatic tight cycles of distinct colours covering all but o(n) vertices of K n ( 3 ) . The same result holds if we replace tight cycles with loose cycles.

      PubDate: 2017-08-31T22:46:30Z
       
  • Packing two graphs of even girth 10
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Wouter Cames van Batenburg, Ross J. Kang
      Two graphs G 1 and G 2 on n vertices are said to pack if there exist injective mappings of their vertex sets into [n] such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollobás and Eldridge and, independently, Catlin, asserts that, if ( Δ ( G 1 ) + 1 ) ( Δ ( G 2 ) + 1 ) ≤ n + 1 , then G 1 and G 2 pack. We consider the validity of this assertion under the additional assumptions that neither G 1 nor G 2 contain a 4-, 6- or 8-cycle, and that Δ ( G 1 ) or Δ ( G 2 ) is large enough (≥940060).

      PubDate: 2017-08-31T22:46:30Z
       
  • Rainbow spanning subgraphs in bounded edge–colourings of graphs with
           large minimum degree
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Pilar Cano, Guillem Perarnau, Oriol Serra
      We study the existence of rainbow perfect matching and rainbow Hamiltonian cycles in edge–colored graphs where every color appears a bounded number of times. We derive asymptotically tight bounds on the minimum degree of the host graph for the existence of such rainbow spanning structures. The proof uses a probabilisitic argument combined with switching techniques.

      PubDate: 2017-08-31T22:46:30Z
       
  • Computing the number of realizations of a Laman graph
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Jose Capco, Matteo Gallet, Georg Grasegger, Christoph Koutschan, Niels Lubbes, Josef Schicho
      Laman graphs model planar frameworks which are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. In a recent paper we provide a recursion formula for this number of realizations using ideas from algebraic and tropical geometry. Here, we present a concise summary of this result focusing on the main ideas and the combinatorial point of view.

      PubDate: 2017-08-31T22:46:30Z
       
  • ν-Tamari lattices via subword complexes
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Cesar Ceballos, Arnau Padrol, Camilo Sarmiento
      We show that the ν-Tamari lattices of Préville-Ratelle and Viennot can obtained as the duals of certain subword complexes. This generalizes a known result for the classical Tamari lattice, provides a simple description of the lattice property using certain bracket vectors of ν-trees, and gives (conjectural) insight on the geometry of more general objects in terms of polytopal subdivisions of multiassociahedra.

      PubDate: 2017-08-31T22:46:30Z
       
  • Combinatorial Problems on H-graphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Steven Chaplick, Peter Zeman
      Biró, Hujter, and Tuza introduced the concept of H-graphs (1992), intersection graphs of connected subgraphs of a subdivision of a fixed graph H. They naturally generalize many important classes of graphs. We continue their study by considering coloring, clique, and isomorphism problems. We show that if H contains a certain multigraph as a minor, then H-graphs are GI-complete and the clique problem is APX-hard. Also, when H is a cactus the clique problem can be solved in polynomial time and when a graph G has a Helly H-representation, the clique problem can be solved in polynomial time. We use treewidth to show that both the k-clique and list k-coloring problems are FPT on H-graphs. These results also apply to treewidth-bounded classes where treewidth is bounded by a function of the clique number.

      PubDate: 2017-08-31T22:46:30Z
       
  • On universal partial words
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Herman Z.Q. Chen, Sergey Kitaev, Torsten Mütze, Brian Y. Sun
      A universal word for a finite alphabet A and some integer n ≥ 1 is a word over A such that every word of length n appears exactly once as a (consecutive) subword. It is well-known and easy to prove that universal words exist for any A and n. In this work we initiate the systematic study of universal partial words. These are words that in addition to the letters from A may contain an arbitrary number of occurrences of a special ‘joker’ symbol ⋄ ∉ A , which can be substituted by any symbol from A. For example, u = 0 ⋄ 011100 is a universal partial word for the binary alphabet A = { 0 , 1 } and for n = 3 (e.g., the first three letters of u yield the subwords 000 and 010). We present results on the existence and non-existence of universal partial words in different situations (depending on the number of ⋄s and their positions), including various explicit constructions. We also provide numerous examples of universal partial words that we found with the help of a computer.

      PubDate: 2017-08-31T22:46:30Z
       
  • On the difference between hamilton cycles and 2-factors with a prescribed
           number of cycles
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Shuya Chiba
      For a vertex subset X of a graph G, let Δ 2 ( X ) be the maximum degree sum of two distinct vertices of X. In this paper, we give the following result: Let k be a positive integer, and let G be an m-connected graph of order n ≥ 5 k − 2 . If Δ 2 ( X ) ≥ n for every independent set X of size ⌈ m / k ⌉ + 1 in G, then G has a 2-factor with exactly k cycles. This is a common generalization of the results obtained by Brandt et al. [Degree conditions for 2-factors, J. Graph Theory 24 (1997), 165–173] and Yamashita [On degree sum conditions for long cycles and cycles through specified vertices, Discrete Math. 308 (2008), 6584–6587], respectively.

      PubDate: 2017-08-31T22:46:30Z
       
  • Chi-boundedness of graph classes excluding wheel vertex-minors
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Hojin Choi, O-joung Kwon, Sang-il Oum, Paul Wollan
      A class of graphs is χ-bounded if there exists a function f : N → N such that for every graph G in the class and an induced subgraph H of G, if H has no clique of size q + 1 , then the chromatic number of H is less than or equal to f(q). We denote by W n the wheel graph on n + 1 vertices. We show that the class of graphs having no vertex-minor isomorphic to W n is χ-bounded. This generalizes several previous results; χ-boundedness for circle graphs, for graphs having no W 5 vertex-minors, and for graphs having no fan vertex-minors.

      PubDate: 2017-08-31T22:46:30Z
       
  • On the number of r-transitive orientations of G(n,p)
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): M. Collares, Y. Kohayakawa, R. Morris, G.O. Mota
      We study the number of orientations T r ( n , p ) of the binomial random graph G ( n , p ) in which every copy of K r is transitive. We give the correct order of growth of log 2 ⁡ T r ( n , p ) up to polylogarithmic factors. In particular, this significantly improves a result of Allen, Kohayakawa, Mota and Parente on T 3 ( n , p ) .

      PubDate: 2017-08-31T22:46:30Z
       
  • Stability of extremal hypergraphs with applications to an edge-coloring
           problem
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Lucas de Oliveira Contiero, Carlos Hoppen, Hanno Lefmann, Knut Odermann
      We obtain sharper stability results for hypergraphs that avoid a copy of an expanded complete 2-graph and for hypergraphs that avoid a Fan subhypergraph. We apply this to an edge-coloring problem on uniform hypergraphs, where we wish to find an n-vertex hypergraph with the largest number of colorings avoiding a rainbow copy of a fixed hypergraph F.

      PubDate: 2017-08-31T22:46:30Z
       
  • Threshold functions for small subgraphs: an analytic approach
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Gwendal Collet, Élie de Panafieu, Danièle Gardy, Bernhard Gittenberger, Vlady Ravelomanana
      We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to describe the possible overlapping of copies.

      PubDate: 2017-08-31T22:46:30Z
       
  • Homological connectedness of random hypergraphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Oliver Cooley, Penny Haxell, Mihyun Kang, Philipp Sprüssel
      We consider simplicial complexes that are generated from the binomial random 3-uniform hypergraph by taking the downward-closure. We determine when this simplicial complex is homologically connected, meaning that its first homology group with coefficients in F2 vanishes and the zero-th homology group is isomorphic to F2. Although this is not intrinsically a monotone property, we show that it has a single sharp threshold, and indeed prove a hitting time result relating the connectedness to the disappearance of the last minimal obstruction.

      PubDate: 2017-08-31T22:46:30Z
       
  • Grid Ramsey problem
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Jan Corsten
      The grid Ramsey number G(r) is the smallest number n such that every edgecolouring of the grid graph Γ n , n : = K n × K n with r colours induces a rectangle whose parallel edges receive the same colour. We show G ( r ) ≤ r ( r + 1 2 ) − ( 1 / 4 − o ( 1 ) ) r ( r 2 ) + 1 slightly improving the currently best known upper bound due to Gyárfás.

      PubDate: 2017-08-31T22:46:30Z
       
  • A simple approach for lower-bounding the distortion in any Hyperbolic
           embedding
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): David Coudert, Guillaume Ducoffe
      We answer open questions of [Verbeek and Suri, SOCG'14] on the relationships between Gromov hyperbolicity and the optimal stretch of graph embeddings in Hyperbolic space. Then, based on the relationships between hyperbolicity and Cops and Robber games, we turn necessary conditions for a graph to be Cop-win into sufficient conditions for a graph to have a large hyperbolicity (and so, no low-stretch embedding in Hyperbolic space). In doing so we derive lower-bounds on the hyperbolicity in various graph classes – such as Cayley graphs, distance-regular graphs and generalized polygons, to name a few. It partly fills in a gap in the literature on Gromov hyperbolicity, for which few lower-bound techniques are known.

      PubDate: 2017-08-31T22:46:30Z
       
  • Contracting Bipartite Graphs to Paths and Cycles
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Konrad K. Dabrowski, Daniël Paulusma
      Testing if a given graph G contains the k-vertex path P k as a minor or as an induced minor is trivial for every fixed integer k ≥ 1 . The situation changes for the problem of checking if a graph can be modified into P k by using only edge contractions. In this case the problem is known to be NP-complete even if k = 4 . This led to an intensive investigation for testing contractibility on restricted graph classes. We focus on bipartite graphs. Heggernes, van 't Hof, Lévêque and Paul proved that the problem stays NP-complete for bipartite graphs if k = 6 . We strengthen their result from k = 6 to k = 5 . We also show that the problem of contracting a bipartite graph to the 6-vertex cycle C 6 is NP-complete. The cyclicity of a graph is the length of the longest cycle the graph can be contracted to. As a consequence of our second result, determining the cyclicity of a bipartite graph is NP-hard.

      PubDate: 2017-08-31T22:46:30Z
       
  • Tight bounds on the coefficients of partition functions via stability
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Ewan Davies, Matthew Jenssen, Barnaby Roberts, Will Perkins
      We show how to use the recently-developed occupancy method and stability results that follow easily from the method to obtain extremal bounds on the individual coefficients of the partition functions over various classes of bounded degree graphs. As applications, we prove new bounds on the number of independent sets and matchings of a given size in regular graphs. For large enough graphs and almost all sizes, the bounds are tight and confirm the Upper Matching Conjecture of Friedland, Krop, and Markström, and a conjecture of Kahn on independent sets for a wide range of parameters. Additionally we prove tight bounds on the number of q-colorings of cubic graphs with a given number of monochromatic edges, and tight bounds on the number of independent sets of a given size in cubic graphs of girth at least 5.

      PubDate: 2017-08-31T22:46:30Z
       
  • Pebble Games and Cospectral Graphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Anuj Dawar, Simone Severini, Octavio Zapata
      Two graphs are cospectral if their respective adjacency matrices have the same multiset of eigenvalues. Cospectrality is an equivalence relation on graphs with many interesting facets. Isomorphic graphs are necessarily cospectral but the converse is not always true, thus cospectrality is a coarser relation than graph isomorphism. Here we study cospectrality from the point of view of pebble games, which are certain type of combinatorial games used in Finite Model Theory to capture the notion of elementary equivalence induced by various logic.

      PubDate: 2017-08-31T22:46:30Z
       
  • On avoding r-repetitions in R2
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Michal Dębski, Jarosław Grytczuk, Urszula Pastwa, Barbara Pilat, Joanna Sokół, Michał Tuczyński, Przemysław Wenus, Krzysztof Węsek
      We say that a coloring of R 2 is line k-nonrepetitive if we will never encounter the same sequence of colors k times in a row when going along any straight line with steps of length 1 unit. This notion is closely related to square- and cube-free words, introduced by Thue. We show that there exists a line 40-nonrepetitive coloring of the plane with only 2 colors. Moreover, we generalize this result for higher dimensions and more general patterns. It complements recent results concerning line 2-nonrepetitive colorings of the plane.

      PubDate: 2017-08-31T22:46:30Z
       
  • On Star Decompositions of Random Regular Graphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Michelle Delcourt, Luke Postle
      Barát and Thomassen Conjectured in 2006 that the edges of every planar 4-regular 4-edge-connected graph can be decomposed into copies of the star with 3 leaves. Shortly afterward, Lai constructed a counterexample to this conjecture. Using the small subgraph conditioning method of Robinson and Wormald, we prove that a random 4-regular graph has an S 3-decomposition asymptotically almost surely, provided that the number of vertices is divisible by 3.

      PubDate: 2017-08-31T22:46:30Z
       
  • On the List Coloring Version of Reed's Conjecture
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Michelle Delcourt, Luke Postle
      The chromatic number of a graph is bounded below by its clique number and from above by its maximum degree plus one. In 1998, Reed conjectured that the chromatic number is at most halfway in between these trivial lower and upper bounds. Moreover, Reed proved that its at most some non-trivial convex combination of the two bounds. In 2012, King and Reed produced a short proof that, provided the maximum degree is large enough, a combination of 1/130,000 suffices. Recently Bonamy, Perrett, and the second author improved this to 1/26. It is natural to wonder if similar results hold for the list chromatic number. Unfortunately, previous techniques for ordinary coloring do not extend to list coloring. In this paper, we overcome these hurdles by introducing several new ideas. Our main result is that the list chromatic number is at most some non-trivial convex combination of the clique number and the maximum degree plus one. Furthermore, we show that for large enough maximum degree, that a combination of 1/13 suffices. Note that this also improves on the best known results for ordinary coloring.

      PubDate: 2017-08-31T22:46:30Z
       
  • Two-layer Drawings of Bipartite Graphs
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Ajit A. Diwan, Bodhayan Roy, Subir Kumar Ghosh
      We give a polynomial-time algorithm to decide whether a connected bipartite graph admits a two-layer drawing in the plane such that a specified subset of pairs of disjoint edges cross. We consider the problem of deciding whether there exists such a drawing in which a specified subset of triples of pairwise crossing edges are concurrent. We give a necessary condition for the same and conjecture that it is sufficient.

      PubDate: 2017-08-31T22:46:30Z
       
  • First steps in combinatorial optimization on graphons: Matchings
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Martin Doležal, Jan Hladký, Ping Hu, Diana Piguet
      Much of discrete optimization concerns problems whose underlying structures are graphs. Here, we translate the theory around the maximum matching problem to the setting of graphons. We study continuity properties of the thus defined matching ratio, limit versions of matching polytopes and vertex cover polytopes, and deduce a version of the LP duality for the problem of maximum fractional matching in the graphon setting.

      PubDate: 2017-08-31T22:46:30Z
       
  • The evolution of random graphs on surfaces
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Chris Dowden, Mihyun Kang, Philipp Sprüssel
      For integers g , m ≥ 0 and n > 0 , let S g ( n , m ) denote the graph taken uniformly at random from the set of all graphs on { 1 , 2 , … , n } with exactly m = m ( n ) edges and with genus at most g. We use counting arguments to investigate the components, subgraphs, maximum degree, and largest face size of S g ( n , m ) , finding that there is often different asymptotic behaviour depending on the ratio m n .

      PubDate: 2017-08-31T22:46:30Z
       
  • Exponentially many nowhere-zero Z3-, Z4-, and Z6-flows
    • Abstract: Publication date: August 2017
      Source:Electronic Notes in Discrete Mathematics, Volume 61
      Author(s): Zdeněk Dvořák, Bojan Mohar, Robert Šámal
      We prove that, in several settings, a graph has exponentially many nowhere-zero flows. Our results may be seen as a counting alternative to the well-known proofs of existence of Z 3 -, Z 4 -, and Z 6 -flows. In the dual setting, proving exponential number of 3-colorings of planar triangle-free graphs is a related open question due to Thomassen.

      PubDate: 2017-08-31T22:46:30Z
       
 
 
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