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On the Chromatic Number of Random Graphs with a Fixed Degree Sequence

Published online by Cambridge University Press:  01 September 2007

ALAN FRIEZE ,
MICHAEL KRIVELEVICH  and
CLIFF SMYTH
ALAN FRIEZE
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA15213, USA (e-mail: alan@random.math.cmu.edu)
MICHAEL KRIVELEVICH
Affiliation:
Department of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: krivelev@post.tau.ac.il)
CLIFF SMYTH
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (e-mail: csmyth@math.mit.edu)
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Abstract

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Let d=1≤d1≤ d2≤···.≤ dn be a non-decreasing sequence of n positive integers, whose sum is even. Let $\mathbb G_{n,{\bf d}$ denote the set of graphs with vertex set [n]={1,2,. . .., n} in which the degree of vertex i is di. Let Gn,d be chosen uniformly at random from $\mathbb G_{n,{\bf d}$. Let d=(d1+d2+···.+dn)/n be the average degree. We give a condition on d under which we can show that w.h.p. the chromatic number of $\mathbb G_{n,{\bf d}$ is Θ(d/ln d). This condition is satisfied by graphs with exponential tails as well those with power law tails.

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 5 , September 2007 , pp. 733 - 746
Copyright
Copyright © Cambridge University Press 2007

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