Reconfiguration of colorable sets in classes of perfect graphs

Takehiro Ito, Yota Otachi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

A set of vertices in a graph is c-colorable if the subgraph induced by the set has a proper c-coloring. In this paper, we study the problem of finding a step-by-step transformation (reconfiguration) between two c-colorable sets in the same graph. This problem generalizes the well-studied Independent Set Reconfiguration problem. As the first step toward a systematic understanding of the complexity of this general problem, we study the problem on classes of perfect graphs. We first focus on interval graphs and give a combinatorial characterization of the distance between two c-colorable sets. This gives a linear-time algorithm for finding an actual shortest reconfiguration sequence for interval graphs. Since interval graphs are exactly the graphs that are simultaneously chordal and co-comparability, we then complement the positive result by showing that even deciding reachability is PSPACE-complete for chordal graphs and for co-comparability graphs. The hardness for chordal graphs holds even for split graphs. We also consider the case where c is a fixed constant and show that in such a case the reachability problem is polynomial-time solvable for split graphs but still PSPACE-complete for co-comparability graphs. The complexity of this case for chordal graphs remains unsettled. As by-products, our positive results give the first polynomial-time solvable cases (split graphs and interval graphs) for Feedback Vertex Set Reconfiguration.

Original languageEnglish
Title of host publication16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
EditorsDavid Eppstein
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages271-2713
Number of pages2443
ISBN (Electronic)9783959770682
DOIs
Publication statusPublished - 2018 Jun 1
Event16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018 - Malmo, Sweden
Duration: 2018 Jun 182018 Jun 20

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume101
ISSN (Print)1868-8969

Other

Other16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
CountrySweden
CityMalmo
Period18/6/1818/6/20

Keywords

  • Colorable set
  • Perfect graph
  • Phrases reconfiguration

ASJC Scopus subject areas

  • Software

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  • Cite this

    Ito, T., & Otachi, Y. (2018). Reconfiguration of colorable sets in classes of perfect graphs. In D. Eppstein (Ed.), 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018 (pp. 271-2713). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 101). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SWAT.2018.27