On the approximation of Min Split-coloring and Min Cocoloring

Marc Demange (1) , Tinaz Ekim (2) , Dominique de Werra (2)

1 ESSEC Business School
2 Institute of Mathematics -ROSE

We consider two problems, namely Min Split-coloring and Min Cocoloring, that generalize the classical Min Coloring problem by allowing to use not only stable sets but also cliques to cover all the vertices of a given graph. We prove the NPhardness of some cases. We derive approximation results for Min Split-coloring and Min Cocoloring in line graphs, comparability graphs and general graphs. This provides to our knowledge the first approximation results for Min Split-coloring since it was defined only very recently [13, 8, 9]. Also, we provide some results on the approximability of Min Cocoloring and comparisons with Min Split-coloring and Min Coloring.

Mots clés: Split-coloring; cocoloring; line graphs; approximation

Domaines: Complexité [cs.CC]; Recherche opérationnelle [math.OC]

Marc Demange, Tinaz Ekim, Dominique de Werra. On the approximation of Min Split-coloring and Min Cocoloring. 2006. ⟨hal-00116689⟩