|Author||McKay, Brendan D.|
|Date of Submission||2010-02-16|
|Subject Domain (in DDC)||Natural sciences & mathematics ♦ Mathematics|
|Subject Keyword||Mathematics - Combinatorics ♦ Mathematics - Probability ♦ 05C80 (Primary) ♦ 60B20 (Secondary) ♦ 05C30 ♦ math|
|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).|
|Learning Resource Type||Article|
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