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Colouring Random 4-Regular Graphs

Published online by Cambridge University Press:  01 March 2007

LINGSHENG SHI  and
NICHOLAS WORMALD
LINGSHENG SHI
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, CanadaN2L 3G1 (e-mail: lshi@math.tsinghua.edu.cn, nwormald@uwaterloo.ca)
NICHOLAS WORMALD
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo ON, CanadaN2L 3G1 (e-mail: lshi@math.tsinghua.edu.cn, nwormald@uwaterloo.ca)
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Abstract

We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3-colours a random 4-regular graph. The analysis includes use of the differential equation method, and exponential bounds on the tail of random variables associated with branching processes. A substantial part of the analysis applies to random d-regular graphs in general.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 16 , Issue 2 , March 2007 , pp. 309 - 344
Copyright
Copyright © Cambridge University Press 2006

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