Journal of Applied Probability
- J. Appl. Probab.
- Volume 51A (2014), 123-137.
The probability that a random multigraph is simple. II
Consider a random multigraph G* with given vertex degrees d1, . . ., dn, constructed by the configuration model. We give a new proof of the fact that, asymptotically for a sequence of such multigraphs with the number of edges ½∑idi → ∞, the probability that the multigraph is simple stays away from 0 if and only if ∑idi = O(∑idi). The new proof uses the method of moments, which makes it possible to use it in some applications concerning convergence in distribution. Corresponding results for bipartite graphs are included.
J. Appl. Probab., Volume 51A (2014), 123-137.
First available in Project Euclid: 2 December 2014
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Janson, Svante. The probability that a random multigraph is simple. II. J. Appl. Probab. 51A (2014), 123--137. doi:10.1239/jap/1417528471. https://projecteuclid.org/euclid.jap/1417528471