Graph coloring with rejection

Leah Epstein, Asaf Levin, Gerhard J. Woeginger

Research output: Contribution to journalArticlepeer-review


We consider the following vertex coloring problem. We are given an undirected graph G=(V,E), where each vertex v is associated with a penalty rejection cost rv. We need to choose a subset of vertices, V′, and to find a proper coloring of the induced subgraph of G over V′. We are interested in both the number of colors used to color the vertices of V′, and in the total rejection cost of all other vertices. The goal is to minimize the sum of these two amounts. In this paper we consider both the online and the offline versions of this problem. In the online version, vertices arrive one at a time, revealing the rejection cost of the current vertex and the set of edges connecting it to previously revealed vertices. We also consider the classical online coloring problem on bounded degree graphs and on (k+1)-claw free graphs.

Original languageEnglish
Pages (from-to)439-447
Number of pages9
JournalJournal of Computer and System Sciences
Issue number2
StatePublished - Mar 2011


  • Approximation algorithms
  • Graph coloring
  • Online algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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