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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.