On maximum matchings in almost regular graphs
نویسندگان
چکیده
منابع مشابه
On 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...
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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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2014
ISSN: 0012-365X
DOI: 10.1016/j.disc.2013.11.019