Clique coloring of dense random graphs

Noga Alon; Michael Krivelevich

doi:https://doi.org/10.1002/jgt.22222

Clique coloring of dense random graphs

Noga Alon, Michael Krivelevich

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

The clique chromatic number of a graph G=(V.E) is the minimum number of colors in a vertex coloring so that no maximal (with respect to containment) clique is monochromatic. We prove that the clique chromatic number of the binomial random graph G=G(n,1/2) is, with high probability, Ω(log n). This settles a problem of McDiarmid, Mitsche, and Prałat who proved that it is O(log n) with high probability.

Original language	English
Pages (from-to)	428-433
Number of pages	6
Journal	Journal of Graph Theory
Volume	88
Issue number	3
DOIs	https://doi.org/10.1002/jgt.22222
State	Published - Jul 2018

Keywords

cliques
coloring
random graphs

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.1002/jgt.22222

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abstract = "The clique chromatic number of a graph G=(V.E) is the minimum number of colors in a vertex coloring so that no maximal (with respect to containment) clique is monochromatic. We prove that the clique chromatic number of the binomial random graph G=G(n,1/2) is, with high probability, Ω(log n). This settles a problem of McDiarmid, Mitsche, and Pra{\l}at who proved that it is O(log n) with high probability.",

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AB - The clique chromatic number of a graph G=(V.E) is the minimum number of colors in a vertex coloring so that no maximal (with respect to containment) clique is monochromatic. We prove that the clique chromatic number of the binomial random graph G=G(n,1/2) is, with high probability, Ω(log n). This settles a problem of McDiarmid, Mitsche, and Prałat who proved that it is O(log n) with high probability.

KW - cliques

KW - coloring

KW - random graphs

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DO - https://doi.org/10.1002/jgt.22222

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EP - 433

JO - Journal of Graph Theory

JF - Journal of Graph Theory

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ER -

Clique coloring of dense random graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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