Results 1 to 10 of about 2,022 (201)
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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Near-Perfect Matchings on Cylinders Cm × Pn of Odd Order [PDF]
EPJ Web of Conferences, 2018 A close relationship was established between the number of perfect and nearperfect matchings on cylinders Cm×Pn. Generating functions are obtained for the number of near-perfect matchings in these graphs for fixed odd m ≤ 13. A conjecture is put forth on
Perepechko Sergey N.
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Perfect Matchings in Random Octagonal Chain Graphs
Journal of Mathematics, 2021 A perfect matching of a (molecule) graph G is a set of independent edges covering all vertices in G. In this paper, we establish a simple formula for the expected value of the number of perfect matchings in random octagonal chain graphs and present the ...
Shouliu Wei +4 more
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Bichromatic Perfect Matchings with Crossings
, 2023 Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023)
Oswin Aichholzer +4 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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