Perfect graphs of arbitrarily large clique-chromatic number

Pierre Charbit (1, 2) , Irena Penev (3) , Stéphan Thomassé (4, 5) , Nicolas Trotignon (4)

1 GANG - Networks, Graphs and Algorithms
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 LIP - Laboratoire de l'Informatique du Parallélisme
4 MC2 - Modèles de calcul, Complexité, Combinatoire
5 IUF - Institut universitaire de France

We prove that there exist perfect graphs of arbitrarily large clique-chromatic number. These graphs can be obtained from cobipartite graphs by repeatedly gluing along cliques. This negatively answers a question raised by Duffus et al. (1991) [5].

Mots clés: clique; coloring; Perfect graph

Domaines: Mathématiques [math]; Informatique [cs]

Pierre Charbit, Irena Penev, Stéphan Thomassé, Nicolas Trotignon. Perfect graphs of arbitrarily large clique-chromatic number. Journal of Combinatorial Theory, Series B, 2016, 116, pp.456-464. ⟨10.1016/j.jctb.2015.09.008⟩. ⟨hal-01324052⟩