A critical point for random graphs with a given degree sequence

Authors:
Michael Molloy;Bruce Reed
Affiliations:
Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213;Equipe Combinatoire, CNRS, Universite Pierre et Marie Curie, Paris, France
Venue:
Random Structures & Algorithms
Year:
1995

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Abstract

Given a sequence of nonnegative real numbers λ0, λ1… which sum to 1, we consider random graphs having approximately λi n vertices of degree i. Essentially, we show that if Σ i(i - 2)λi 0, then such graphs almost surely have a giant component, while if Σ i(i -2)λ. Gn,p,Gn.M, and other well-known models of random graphs. There are also applications related to the chromatic number of sparse random graphs. © 1995 Wiley Periodicals, Inc.