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The Coloring Reconfiguration Problem on Specific Graph Classes

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Combinatorial Optimization and Applications (COCOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10627))

Abstract

We study the problem of transforming one (vertex) k-coloring of a graph into another one by changing only one vertex color assignment at a time, while at all times maintaining a k-coloring, where k denotes the number of colors. This decision problem is known to be PSPACE-complete even for bipartite graphs and any fixed constant \(k \ge 4\). In this paper, we study the problem from the viewpoint of graph classes. We first show that the problem remains PSPACE-complete for chordal graphs even if the number of colors is a fixed constant. We then demonstrate that, even when the number of colors is a part of input, the problem is solvable in polynomial time for several graph classes, such as split graphs and trivially perfect graphs.

This work is partially supported by JST CREST Grant Number JPMJCR1402, and by JSPS KAKENHI Grant Numbers JP16J02175, JP16K00003, and JP16K00004, Japan.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Aoba-yama 6-6-05, Sendai, 980-8579, Japan

    Tatsuhiko Hatanaka, Takehiro Ito & Xiao Zhou

Authors
  1. Tatsuhiko Hatanaka
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  2. Takehiro Ito
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  3. Xiao Zhou
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Corresponding author

Correspondence to Tatsuhiko Hatanaka .

Editor information

Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Hatanaka, T., Ito, T., Zhou, X. (2017). The Coloring Reconfiguration Problem on Specific Graph Classes. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10627. Springer, Cham. https://doi.org/10.1007/978-3-319-71150-8_15

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  • DOI: https://doi.org/10.1007/978-3-319-71150-8_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71149-2

  • Online ISBN: 978-3-319-71150-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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