Reconfiguration of colorable sets in classes of perfect graphs

Takehiro Ito, Yota Otachi

研究成果: Conference contribution

1 引用 (Scopus)

抜粋

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.

元の言語English
ホスト出版物のタイトル16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
編集者David Eppstein
出版者Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ページ271-2713
ページ数2443
ISBN(電子版)9783959770682
DOI
出版物ステータスPublished - 2018 6 1
イベント16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018 - Malmo, Sweden
継続期間: 2018 6 182018 6 20

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
101
ISSN(印刷物)1868-8969

Other

Other16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018
Sweden
Malmo
期間18/6/1818/6/20

ASJC Scopus subject areas

  • Software

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  • これを引用

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