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- W2118233485 abstract "Let G = G ( n ) be a randomly chosen k -edge-coloured k -regular graph with 2 n vertices, where k = k ( n ). Such a graph can be obtained from a random set of k edge-disjoint perfect matchings of K 2 n . Let h = h ( n ) be a graph with m = m ( n ) edges such that m 2 + mk = o ( n ). Using a switching argument, we find an asymptotic estimate of the expected number of subgraphs of G isomorphic to h . Isomorphisms may or may not respect the edge colouring, and other generalizations are also presented. Special attention is paid to matchings and cycles. The results in this paper are essential to a forthcoming paper of McLeod in which an asymptotic estimate for the number of k -edge-coloured k -regular graphs for k = o ( n 5/6 ) is found." @default.
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- W2118233485 date "2009-07-01" @default.
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- W2118233485 title "Subgraphs of Randomk-Edge-Colouredk-Regular Graphs" @default.
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- W2118233485 doi "https://doi.org/10.1017/s0963548309009882" @default.
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