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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© 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
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