Clique coloring of dense random graphs | Zendy

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Clique coloring of dense random graphs

Author(s) -

Alon Noga,

Krivelevich Michael

Publication year - 2018

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.22222

Subject(s) - mathematics , combinatorics , monochromatic color , clique number , clique , vertex (graph theory) , fractional coloring , clique graph , brooks' theorem , random graph , discrete mathematics , graph coloring , chromatic scale , binomial (polynomial) , graph , chordal graph , 1 planar graph , graph power , line graph , statistics , botany , biology

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.

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