Journal of Applied Probability

The probability that a random multigraph is simple. II

Svante Janson

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51A (2014), 123-137.

Dates
First available in Project Euclid: 2 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1417528471

Digital Object Identifier
doi:10.1239/jap/1417528471

Mathematical Reviews number (MathSciNet)
MR3317354

Zentralblatt MATH identifier
1309.05162

Subjects
Primary: 05C80: Random graphs [See also 60B20] 05C30: Enumeration in graph theory 60C05: Combinatorial probability

Keywords
Configuration model random multigraph random bipartite graph

Citation

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


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