Clique coloring of binomial random graphs

Colin Mcdiarmid (1) , Dieter Mitsche (2) , Paweł Prałat

1 Department of Statistics [Oxford]
2 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]

Colin Mcdiarmid, Dieter Mitsche, Paweł Prałat. Clique coloring of binomial random graphs. Random Structures and Algorithms, 2018, ⟨10.1002/rsa.20804⟩. ⟨hal-02083918⟩