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Conflict-Free Colouring of Graphs

Published online by Cambridge University Press:  29 November 2013

ROMAN GLEBOV
Affiliation:
Department of Mathematics, ETH, 8092 Zurich, Switzerland and Mathematics Institute and DIMAP, University of Warwick, Coventry CV4 7AL, UK (e-mail: roman.l.glebov@gmail.com)
TIBOR SZABÓ
Affiliation:
Institute of Mathematics, Free University of Berlin, 14195 Berlin, Germany (e-mail: szabo@math.fu-berlin.de)
GÁBOR TARDOS
Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary and Zhejiang Normal University, Jinhua, China (e-mail: tardos@renyi.hu)

Abstract

We study the conflict-free chromatic number χCF of graphs from extremal and probabilistic points of view. We resolve a question of Pach and Tardos about the maximum conflict-free chromatic number an n-vertex graph can have. Our construction is randomized. In relation to this we study the evolution of the conflict-free chromatic number of the Erdős–Rényi random graph G(n,p) and give the asymptotics for p = ω(1/n). We also show that for p ≥ 1/2 the conflict-free chromatic number differs from the domination number by at most 3.

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Paper
Copyright
Copyright © Cambridge University Press 2013 

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References

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