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A Random Recolouring Method for Graphs and Hypergraphs

Published online by Cambridge University Press:  12 September 2008

Colin McDiarmid
Colin McDiarmid
Affiliation:
Department of Statistics, University of Oxford
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Abstract

We consider a simple randomised algorithm that seeks a weak 2-colouring of a hypergraph H; that is, it tries to 2-colour the points of H so that no edge is monochromatic. If H has a particular well-behaved form of such a colouring, then the method is successful within expected number of iterations O(n3) when H has n points. In particular, when applied to a graph G with n nodes and chromatic number 3, the method yields a 2-colouring of the vertices such that no triangle is monochromatic in expected time O(n4).

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 3 , September 1993 , pp. 363 - 365
Copyright
Copyright © Cambridge University Press 1993

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