Results 61 to 70 of about 2,022 (201)
Further results on enumeration of perfect matchings of Cartesian product graphs
Open MathematicsCounting perfect matchings is an interesting and challenging combinatorial task. It has important applications in statistical physics and chemistry. As the general problem is #P-complete, it is usually tackled by randomized heuristics and approximation ...
Wu Tingzeng, Zeng Xiaolin
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Counting and enumerating crossing-free geometric graphs
Journal of Computational Geometry, 2017 We describe a framework for constructing data structures which allow fast counting and enumeration of various types of crossing-free geometric graphs on a planar point set.
Manuel Wettstein
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More Aspects of Arbitrarily Partitionable Graphs
Discussiones Mathematicae Graph Theory, 2022 A graph G of order n is arbitrarily partitionable (AP) if, for every sequence (n1, . . ., np) partitioning n, there is a partition (V1, . . ., ,Vp) of V (G) such that G[Vi] is a connected ni-graph for i = 1, . . ., p.
Bensmail Julien, Li Binlong
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The enumeration of near-perfect matchings of factor-critical graphs
, 2002 A matching of a graph is a near-perfect matching if it covers all but one vertex. A connected graph G is said to be factor-critical if G−v has perfect matchings for every vertex v of G.
Liu, Yan +3 more
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On Variable Sum Exdeg Indices of Quasi-Tree Graphs and Unicyclic Graphs
Discrete Dynamics in Nature and Society, 2020 In this work, by using the properties of the variable sum exdeg indices and analyzing the structure of the quasi-tree graphs and unicyclic graphs, the minimum and maximum variable sum exdeg indices of quasi-tree graphs and quasi-tree graphs with perfect ...
Xiaoling Sun, Jianwei Du
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Cluster algebras of unpunctured surfaces and snake graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect matchings of a ...
Gregg Musiker, Ralf Schiffler
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Matching Preclusion of the Generalized Petersen Graph
Theory and Applications of Graphs, 2019 The matching preclusion number of a graph with an even number of vertices is the minimum number of edges whose deletion results in a graph with no perfect matchings.
Ajay Arora +2 more
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Perfect matchings after vertex deletions
, 2007 This paper considers some classes of graphs which are easily seen to have many perfect matchings. Such graphs can be considered robust with respect to the property of having a perfect matching if under vertex deletions (with some mild restrictions), the ...
Locke, S.C. +5 more
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Three matching intersection property for matching covered graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 In connection with Fulkerson's conjecture on cycle covers, Fan and Raspaud proposed a weaker conjecture: For every bridgeless cubic graph $G$, there are three perfect matchings $M_1$, $M_2$, and $M_3$ such that $M_1\cap M_2 \cap M_3=\emptyset$.
Hao Lin, Xiumei Wang
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Exponentially many perfect matchings in cubic graphs
, 2011 We show that every cubic bridgeless graph G has at least 2|V(G)|/3656 perfect matchings.
Louis Esperet +12 more
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