Year: 2010
Type: preprint
Abstract: Let d = (d1, d2, ..., dn) be a vector of non-negative integers with even sum. We prove some basic facts about the structure of a random graph with degree sequence d, including the probability of a given subgraph or induced subgraph. Although there are many results of this kind, they are restricted to the sparse case with only a few exceptions. Our focus is instead on the case where the average degree is approximately a constant fraction of n. Our approach is the multidimensional saddle-point method. This extends the enumerative work of McKay and Wormald (1990) and is analogous to the theory developed for bipartite graphs by Greenhill and McKay (arXiv:math/0701600, 2009).
Source: arXiv (Cornell University)
Author: McKay, Brendan D
Institution: Australian National University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953146946