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The t-Improper Chromatic Number of Random Graphs

Published online by Cambridge University Press:  09 September 2009

ROSS J. KANG  and
COLIN McDIARMID
ROSS J. KANG
Affiliation:
School of Computer Science, McGill University, Montréal, Québec, H2A 2A7, Canada (e-mail: [email protected])
COLIN McDIARMID
Affiliation:
Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK (e-mail: [email protected])
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Abstract

We consider the t-improper chromatic number of the Erdős–Rényi random graph Gn,p. The t-improper chromatic number χt(G) is the smallest number of colours needed in a colouring of the vertices in which each colour class induces a subgraph of maximum degree at most t. If t = 0, then this is the usual notion of proper colouring. When the edge probability p is constant, we provide a detailed description of the asymptotic behaviour of χt(Gn,p) over the range of choices for the growth of t = t(n).

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 19 , Issue 1 , January 2010 , pp. 87 - 98
Copyright
Copyright © Cambridge University Press 2009

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