English

Clique colouring of binomial random graphs

Probability 2016-11-08 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.1611.01782,
  title  = {Clique colouring of binomial random graphs},
  author = {Colin McDiarmid and Dieter Mitsche and Pawel Pralat},
  journal= {arXiv preprint arXiv:1611.01782},
  year   = {2016}
}

Comments

25 pages

R2 v1 2026-06-22T16:43:26.132Z