Graph coloring with rejection

Leah Epstein; Asaf Levin; Gerhard J. Woeginger

doi:10.1007/11841036_34

Graph coloring with rejection

Leah Epstein, Asaf Levin, Gerhard J. Woeginger

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 r_ν. 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 language	English
Title of host publication	Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings
Publisher	Springer Verlag
Pages	364-375
Number of pages	12
ISBN (Print)	3540388753, 9783540388753
DOIs	https://doi.org/10.1007/11841036_34
State	Published - 2006
Event	14th Annual European Symposium on Algorithms, ESA 2006 - Zurich, Switzerland Duration: 11 Sep 2006 → 13 Sep 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4168 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	14th Annual European Symposium on Algorithms, ESA 2006
Country/Territory	Switzerland
City	Zurich
Period	11/09/06 → 13/09/06

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/11841036_34

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Epstein, L., Levin, A., & Woeginger, G. J. (2006). Graph coloring with rejection. In Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings (pp. 364-375). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4168 LNCS). Springer Verlag. https://doi.org/10.1007/11841036_34

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title = "Graph coloring with rejection",

abstract = "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.",

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year = "2006",

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series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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pages = "364--375",

booktitle = "Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings",

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note = "14th Annual European Symposium on Algorithms, ESA 2006 ; Conference date: 11-09-2006 Through 13-09-2006",

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Epstein, L, Levin, A & Woeginger, GJ 2006, Graph coloring with rejection. in Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4168 LNCS, Springer Verlag, pp. 364-375, 14th Annual European Symposium on Algorithms, ESA 2006, Zurich, Switzerland, 11/09/06. https://doi.org/10.1007/11841036_34

Graph coloring with rejection. / Epstein, Leah; Levin, Asaf; Woeginger, Gerhard J.
Algorithms, ESA 2006 - 14th Annual European Symposium, Proceedings. Springer Verlag, 2006. p. 364-375 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4168 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Levin, Asaf

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N2 - 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.

AB - 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.

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Graph coloring with rejection

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