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• W2084832642 abstract "The space of permutation pseudographs is a probabilistic model of 2-regular pseudographs on n vertices, where a pseudograph is produced by choosing a permutation σ of {1,2,…, n } uniformly at random and taking the n edges { i ,σ( i )}. We prove several contiguity results involving permutation pseudographs (contiguity is a kind of asymptotic equivalence of sequences of probability spaces). Namely, we show that a random 4-regular pseudograph is contiguous with the sum of two permutation pseudographs, the sum of a permutation pseudograph and a random Hamilton cycle, and the sum of a permutation pseudograph and a random 2-regular pseudograph. (The sum of two random pseudograph spaces is defined by choosing a pseudograph from each space independently and taking the union of the edges of the two pseudographs.) All these results are proved simultaneously by working in a general setting, where each cycle of the permutation is given a nonnegative constant multiplicative weight. A further contiguity result is proved involving the union of a weighted permutation pseudograph and a random regular graph of arbitrary degree. All corresponding results for simple graphs are obtained as corollaries." @default.
• W2084832642 created "2016-06-24" @default.
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• W2084832642 date "2002-05-01" @default.
• W2084832642 modified "2023-10-17" @default.
• W2084832642 title "Permutation Pseudographs and Contiguity" @default.
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• W2084832642 doi "https://doi.org/10.1017/s0963548301005065" @default.
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