Results 1 to 10 of about 622 (259)
Perfect Matchings with Crossings. [PDF]
Algorithmica, 2022 Abstract For sets of n points, n even, in general position in the plane, we consider straight-line drawings of perfect matchings on them. It is well known that such sets admit at least
Aichholzer O +7 more
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On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings [PDF]
The Scientific World Journal, 2014 The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.
Jing-Ming Zhang +2 more
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Solving perfect matchings by frequency-grouped multi-photon events using a silicon chip [PDF]
Nature CommunicationsComputing the number of perfect matchings of a graph is a famous #P-complete problem. In this work, taking the advantages of the frequency dimension of photon, we propose and implement a photonic perfect matching solver, by combining two key techniques ...
Pingyu Zhu +8 more
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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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Tight upper bound on the maximum anti-forcing numbers of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2017 Let $G$ be a simple graph with a perfect matching. Deng and Zhang showed that the maximum anti-forcing number of $G$ is no more than the cyclomatic number.
Lingjuan Shi, Heping Zhang
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Theory and Applications of Graphs, 2022 Given an edge-colored complete graph Kn on n vertices, a perfect (respectively, near-perfect) matching M in Kn with an even (respectively, odd) number of vertices is rainbow if all edges have distinct colors.
Shuhei Saitoh, Naoki Matsumoto, Wei Wu
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Families with no perfect matchings [PDF]
Combinatorial Theory, 2021 We consider families of $k$-subsets of $\{1, \dots, n\}$, where $n$ is a multiple of $k$, which have no perfect matching. An equivalent condition for a family $\mathcal{F}$ to have no perfect matching is for there to be a blocking set, which is a set of $b$ elements of $\{1, \dots, n\}$ that cannot be covered by $b$ disjoint sets in $\mathcal{F}$.
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Perfect Matching Preservers [PDF]
The Electronic Journal of Combinatorics, 2006 For two bipartite graphs $G$ and $G'$, a bijection $\psi: E(G) \rightarrow E(G')$ is called a (perfect) matching preserver provided that $M$ is a perfect matching in $G$ if and only if $\psi(M)$ is a perfect matching in $G'$. We characterize bipartite graphs $G$ and $G'$ which are related by a matching preserver and the matching preservers between them.
Richard A. Brualdi +2 more
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On perfect matchings in matching covered graphs [PDF]
Journal of Graph Theory, 2018 AbstractA graph is matching‐covered if every edge of is contained in a perfect matching. A matching‐covered graph is strongly coverable if, for any edge of , the subgraph is still matching‐covered. An edge subset of a matching‐covered graph is feasible if there exist two perfect matchings and such that , and an edge subset with at least two ...
Jinghua He +3 more
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On two consequences of Berge–Fulkerson conjecture
AKCE International Journal of Graphs and Combinatorics, 2020 The classical Berge–Fulkerson conjecture states that any bridgeless cubic graph admits a list of six perfect matchings such that each edge of belongs to two of the perfect matchings from the list.
Vahan V. Mkrtchyan, Gagik N. Vardanyan
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