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Graph Coloring with Rejection

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

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 r v . 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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Leah Epstein

  2. Department of Statistics, The Hebrew University, 91905, Jerusalem, Israel

    Asaf Levin

  3. Department of Mathematics and Computer Science, TU Eindhoven, P.O. Box 513, 5600, MB Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Leah Epstein
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  2. Asaf Levin
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  3. Gerhard J. Woeginger
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Epstein, L., Levin, A., Woeginger, G.J. (2006). Graph Coloring with Rejection. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_34

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  • DOI: https://doi.org/10.1007/11841036_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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