Weighted coloring: further complexity and approximability results

Bruno Escoffier (1) , Jérôme Monnot (1) , Vangelis Th. Paschos (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

Given a vertex-weighted graph G = (V,E;w), w(v) ≥ 0 for any v ∈ V , we consider a weighted version of the coloring problem which consists in finding a partition S = (S1, . . . , Sk) of the vertex set V of G into stable sets and minimizing k i=1 w(Si) where the weight of S is defined as max{w(v) : v ∈ S}. In this paper, we keep on with the investigation of the complexity and the approximability of this problem by mainly answering one of the questions raised by D. J. Guan and X. Zhu ("A Coloring Problem for Weighted Graphs", Inf. Process. Lett. 61(2):77-81 1997).

Mots clés: Approximation algorithm; NP-complete problems; weighted coloring; interval graphs; line graph of bipartite graphs; partial k-tree

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

Bruno Escoffier, Jérôme Monnot, Vangelis Th. Paschos. Weighted coloring: further complexity and approximability results. 2006. ⟨hal-00116712⟩