Perfect matchings and derangements on graphs
نویسندگان
چکیده
منابع مشابه
Perfect Matchings in Edge-Transitive Graphs
We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
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When we think about markets creating opportunities for interaction between buyers and sellers, there is an implicit network encoding the access between buyers and sellers. In fact, there are several ways to use networks to model buyer-seller interaction, and here we discuss some of them. First, consider the case in which not all buyers have access to all sellers. There could be several reasons ...
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Counting perfect matchings has played a central role in the theory of counting problems. The permanent, corresponding to bipartite graphs, was shown to be #P-complete to compute exactly by Valiant (1979), and a fully polynomial randomized approximation scheme (FPRAS) was presented by Jerrum, Sinclair, and Vigoda (2004) using a Markov chain Monte Carlo (MCMC) approach. However, it has remained a...
متن کاملOn Perfect Matchings in Matching Covered Graphs
Let G be a matching-covered graph, i.e., every edge is contained in a perfect matching. An edge subsetX ofG is feasible if there exists two perfect matchingsM1 andM2 such that |M1∩X| 6≡ |M2∩X| (mod 2). Lukot’ka and Rollová proved that an edge subset X of a regular bipartite graph is not feasible if and only if X is switching-equivalent to ∅, and they further ask whether a non-feasible set of a ...
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Let G be a graph embedded in a surface and let F be a set of even faces of G (faces bounded by a cycle of even length). The resonance graph of G with respect to F, denoted by R(G;F), is a graph such that its vertex set is the set of all perfect matchings of G and two vertices M1 and M2 are adjacent to each other if and only if the symmetric difference M1 ⊕M2 is a cycle bounding some face in F. ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2021
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22658