Abstract
Consider a random multigraph G* with given vertex degrees d1,. . .,dn, constructed by the configuration model. We show that, asymptotically for a sequence of such multigraphs with the number of edges $\tfrac12\sumd\to\infty$, the probability that the multigraph is simple stays away from 0 if and only if $\sumdd=O\bigpar{\sumd}$. This was previously known only under extra assumptions on the maximum degree maxidi. We also give an asymptotic formula for this probability, extending previous results by several authors.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Reference15 articles.
1. The cores of random hypergraphs with a given degree sequence
2. Random Graphs
3. [14] Wormald N. C. (1978) Some problems in the enumeration of labelled graphs. PhD thesis, University of Newcastle.
4. Asymptotics for symmetric 0–1 matrices with prescribed row sums;McKay;Ars Combin.,1985
Cited by
100 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献