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A note on pm-compact bipartite graphs
Discussiones Mathematicae Graph Theory, 2014 A graph is called perfect matching compact (briefly, PM-compact), if its perfect matching graph is complete. Matching-covered PM-compact bipartite graphs have been characterized. In this paper, we show that any PM-compact bipartite graph G with δ (G) ≥ 2
Liu Jinfeng, Wang Xiumei
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On the number of perfect matchings in random polygonal chains
Open Mathematics, 2023 Let GG be a graph. A perfect matching of GG is a regular spanning subgraph of degree one. Enumeration of perfect matchings of a (molecule) graph is interest in chemistry, physics, and mathematics.
Wei Shouliu +3 more
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Exploration of CPCD number for power graph
مجلة بغداد للعلوم, 2023 Recently, complementary perfect corona domination in graphs was introduced. A dominating set S of a graph G is said to be a complementary perfect corona dominating set (CPCD – set) if each vertex in is either a pendent vertex or a support vertex and ...
S. Anuthiya, G. Mahadevan, C. Sivagnanam
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Dyck tilings, linear extensions, descents, and inversions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 Dyck tilings were introduced by Kenyon and Wilson in their study of double-dimer pairings. They are certain kinds of tilings of skew Young diagrams with ribbon tiles shaped like Dyck paths.
Jang Soo Kim +3 more
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Even cycles and perfect matchings in claw-free plane graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Lov{\'a}sz showed that a matching covered graph $G$ has an ear decomposition starting with an arbitrary edge of $G$. Let $G$ be a graph which has a perfect matching.
Shanshan Zhang +2 more
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Questions on the Structure of Perfect Matchings inspired by Quantum Physics [PDF]
, 2019 We state a number of related questions on the structure of perfect matchings. Those questions are inspired by and directly connected to Quantum Physics.
Gu, Xuemei +2 more
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Conditional Strong Matching Preclusion of the Alternating Group Graph
Theory and Applications of Graphs, 2019 The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings.
Mohamad Adballah, Eddie Cheng
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Polynomial-time perfect matchings in dense hypergraphs [PDF]
, 2013 Let $H$ be a $k$-graph on $n$ vertices, with minimum codegree at least $n/k + cn$ for some fixed $c > 0$. In this paper we construct a polynomial-time algorithm which finds either a perfect matching in $H$ or a certificate that none exists.
Keevash, Peter +2 more
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On some Graphs with a Unique Perfect Matching
, 2017 We show that deciding whether a given graph $G$ of size $m$ has a unique perfect matching as well as finding that matching, if it exists, can be done in time $O(m)$ if $G$ is either a cograph, or a split graph, or an interval graph, or claw-free ...
Chaplick, S. +3 more
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A Maximum Resonant Set of Polyomino Graphs
Discussiones Mathematicae Graph Theory, 2016 A polyomino graph P is a connected finite subgraph of the infinite plane grid such that each finite face is surrounded by a regular square of side length one and each edge belongs to at least one square.
Zhang Heping, Zhou Xiangqian
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