The probability that a random multigraph is simple
组合数学
2007-05-23 v1 概率论
摘要
Consider a random multigraph G* with given vertex degrees d_1,...,d_n, contructed by the configuration model. We show that, asymptotically for a sequence of such multigraphs with the number of edges (d_1+...+d_n)/2 tending to infinity, the probability that the multigraph is simple stays away from 0 if and only if \sum d_i^2=O(\sum d_i). This was previously known only under extra assumtions on the maximum degree. We also give an asymptotic formula for this probability, extending previous results by several authors.
引用
@article{arxiv.math/0609802,
title = {The probability that a random multigraph is simple},
author = {Svante Janson},
journal= {arXiv preprint arXiv:math/0609802},
year = {2007}
}
备注
24 pages