Graph coloring with rejection

Leah Epstein, Asaf Levin, Gerhard J. Woeginger

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider the following vertex coloring problem. We are given an undirected graph G = (V, E), where each vertex ν is associated with a penalty rejection cost rν. 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
Title of host publicationAlgorithms, ESA 2006 - 14th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540388753, 9783540388753
StatePublished - 2006
Event14th Annual European Symposium on Algorithms, ESA 2006 - Zurich, Switzerland
Duration: 11 Sep 200613 Sep 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4168 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th Annual European Symposium on Algorithms, ESA 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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