Results and open problems in matchings in regular graphs
نویسندگان
چکیده
منابع مشابه
Results and open problems in matchings in regular graphs
This survey paper deals with upper and lower bounds on the number of k-matchings in regular graphs on N vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower bounds we first survey the known results for bipartite graphs, and their continuous versions as the van der Waerden and Tverberg permanent conjectures and its var...
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This survey paper deals with upper and lower bounds on the number of k-matchings in regular graphs on N vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower bounds we first survey the known results for bipartite graphs, and their continuous versions as the van der Waerden and Tverberg permanent conjectures and its var...
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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: The Electronic Journal of Linear Algebra
سال: 2012
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1577