Clique coloring of binomial random graphs

Authors :: Dieter Mitsche
Paweł Prałat
Colin McDiarmid
Department of Statistics [Oxford]
University of Oxford [Oxford]
Laboratoire Jean Alexandre Dieudonné (JAD)
Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS)
COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Source :: Random Structures and Algorithms, Random Structures and Algorithms, Wiley, 2018, ⟨10.1002/rsa.20804⟩
Publication Year :: 2018
Publisher :: Wiley, 2018.
Abstract: A clique colouring of a graph is a colouring of the vertices so that no maximal clique is monochromatic (ignoring isolated vertices). The smallest number of colours in such a colouring is the clique chromatic number. In this paper, we study the asymptotic behaviour of the clique chromatic number of the random graph G(n,p) for a wide range of edge-probabilities p=p(n). We see that the typical clique chromatic number, as a function of the average degree, forms an intriguing step function.<br />25 pages

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