منابع مشابه
Random Matchings in Regular Graphs
For a simple d-regular graph G, let M be chosen uniformly at random from the set of all matchings of G, and for x ∈ V (G) let p(x) be the probability that M does not cover x. We show that for large d, the p(x)’s and the mean μ and variance σ of |M | are determined to within small tolerances just by d and (in the case of μ and σ) |V (G)|: Theorem For any d-regular graph G, (a) p(x) ∼ d ∀x ∈ V (G...
متن کاملPerfect matchings in regular graphs from eigenvalues
Throughout, G denotes a simple graph of order n (the number of vertices) and size e (the number of edges). The eigenvalues of G are the eigenvalues λi 1 Research partially supported by an NSERC postdoctoral fellowship. 2 Research supported by the Natural Sciences and Engineering Research Council of Canada. Email addresses: [email protected] (Sebastian M. Cioabă), [email protected] (D...
متن کاملOn maximum matchings in almost regular graphs
In 2010, Mkrtchyan, Petrosyan and Vardanyan proved that every graph G with 2 ≤ δ(G) ≤ ∆(G) ≤ 3 contains a maximum matching whose unsaturated vertices do not have a common neighbor, where ∆(G) and δ(G) denote the maximum and minimum degrees of vertices in G, respectively. In the same paper they suggested the following conjecture: every graph G with ∆(G)− δ(G) ≤ 1 contains a maximum matching whos...
متن کاملPerfect Matchings in ε-regular Graphs
A super (d, )-regular graph on 2n vertices is a bipartite graph on the classes of vertices V1 and V2, where |V1| = |V2| = n, in which the minimum degree and the maximum degree are between (d− )n and (d+ )n, and for every U ⊂ V1,W ⊂ V2 with |U | ≥ n, |W | ≥ n, | e(U,W ) |U ||W | − e(V1,V2) |V1||V2| | < . We prove that for every 1 > d > 2 > 0 and n > n0( ), the number of perfect matchings in any ...
متن کاملMatchings in regular graphs from eigenvalues
Article history: Received 6 December 2006 Available online 26 July 2008
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1981
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90006-6