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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 12→∞ , the probability that the multigraph is simple stays away from 0 if and only if =O . 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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Svante Janson (2009) studied this question.
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