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Subgraphs of Dense Random Graphs with Specified Degrees

Published online by Cambridge University Press:  27 January 2011

BRENDAN D. McKAY
BRENDAN D. McKAY*
Affiliation:
School of Computer Science, Australian National University, Canberra ACT 0200, Australia (e-mail: bdm@cs.anu.edu.au)
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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 (2009).

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 3 , May 2011 , pp. 413 - 433
Copyright
Copyright © Cambridge University Press 2011

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