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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).

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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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