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Reconfiguration of Cliques in a Graph

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Book cover Theory and Applications of Models of Computation (TAMC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9076))

Abstract

We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. In particular, the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs.

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Acknowledgments

This work is partially supported by MEXT/JSPS KAKENHI 25106504 and 25330003 (T. Ito), 25104521 and 26540005 (H. Ono), and 24106004 and 25730003 (Y. Otachi).

Author information

Authors and Affiliations

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

    Takehiro Ito

  2. Faculty of Economics, Kyushu University, Hakozaki 6-19-1, Higashi-ku, Fukuoka, 812-8581, Japan

    Hirotaka Ono

  3. School of Information Science, JAIST, Asahidai 1-1, Nomi, Ishikawa, 923-1292, Japan

    Yota Otachi

Authors
  1. Takehiro Ito
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  2. Hirotaka Ono
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  3. Yota Otachi
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Corresponding author

Correspondence to Yota Otachi .

Editor information

Editors and Affiliations

  1. National University of Singapore, Singapore, Singapore

    Rahul Jain

  2. National University of Singapore, Singapore, Singapore

    Sanjay Jain

  3. National University of Singapore, Singapore, Singapore

    Frank Stephan

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Ito, T., Ono, H., Otachi, Y. (2015). Reconfiguration of Cliques in a Graph. In: Jain, R., Jain, S., Stephan, F. (eds) Theory and Applications of Models of Computation. TAMC 2015. Lecture Notes in Computer Science(), vol 9076. Springer, Cham. https://doi.org/10.1007/978-3-319-17142-5_19

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  • DOI: https://doi.org/10.1007/978-3-319-17142-5_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17141-8

  • Online ISBN: 978-3-319-17142-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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