Journal
COMBINATORICS PROBABILITY & COMPUTING
Volume 18, Issue 1-2, Pages 205-225Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0963548308009644
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Consider a random multigraph G* with given vertex degrees d(1),...,d(n), constructed by the configuration model. We show that, asymptotically for a sequence of such multigraphs with the number of edges 1/2 Sigma(i) d(i) -> infinity, the probability that the multigraph is simple stays away from 0 if and only if Sigma(i) d(i)(2) = O (Sigma(i) d(i)). This was previously known only under extra assumptions on the maximum degree max(i) d(i). We also give an asymptotic formula for this probability, extending previous results by several authors.
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