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Journal Articles Random Structures and Algorithms Year : 2021

The jump of the clique chromatic number of random graphs

Abstract

The clique chromatic number of a graph is the smallest number of colors in a vertex coloring so that no maximal clique is monochromatic. In 2016 McDiarmid, Mitsche and Prałat noted that around the clique chromatic number of the random graph changes by when we increase the edge‐probability by , but left the details of this surprising “jump” phenomenon as an open problem. We settle this problem, that is, resolve the nature of this polynomial “jump” of the clique chromatic number of the random graph around edge‐probability . Our proof uses a mix of approximation and concentration arguments, which enables us to (i) go beyond Janson's inequality used in previous work and (ii) determine the clique chromatic number of up to logarithmic factors for any edge‐probability .
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Dates and versions

hal-04619465 , version 1 (21-06-2024)

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Lyuben Lichev, Dieter Mitsche, Lutz Warnke. The jump of the clique chromatic number of random graphs. Random Structures and Algorithms, 2021, 62 (4), pp.1016-1034. ⟨10.1002/rsa.21128⟩. ⟨hal-04619465⟩
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