Clique coloring of dense random graphs

Noga Alon; Michael Krivelevich

doi:10.1002/jgt.22222

Clique coloring of dense random graphs

Noga Alon
, Michael Krivelevich

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

6 Scopus citations

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 - 1 Jul 2018
Externally published	Yes

Keywords

cliques
coloring
random graphs

ASJC Scopus subject areas

Geometry and Topology

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10.1002/jgt.22222

Cite this

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title = "Clique coloring of dense random graphs",

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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AU - Alon, Noga

AU - Krivelevich, Michael

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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/85046907949

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DO - 10.1002/jgt.22222

M3 - Article

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ER -

Clique coloring of dense random graphs

Abstract

Keywords

ASJC Scopus subject areas

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