Weighted Coloring: Further Complexity and Approximability Results

  • Bruno Escoffier
  • Jérôme Monnot
  • Vangelis Th. Paschos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3701)

Abstract

Given a vertex-weighted graph G = (V,E;w), w(v) ≥ 0 for any vV, we consider a weighted version of the coloring problem which consists in finding a partition \({\mathcal S}=(S_{1}...,S_{k})\) of the vertex set V of G into stable sets and minimizing ∑i = 1kw(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).

Keywords

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bruno Escoffier
    • 1
  • Jérôme Monnot
    • 1
  • Vangelis Th. Paschos
    • 1
  1. 1.LAMSADE, CNRS and Université Paris-DauphineParis Cedex 16France

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