Reconfiguration of colorable sets in classes of perfect graphs

Takehiro Ito, Yota Otachi

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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 (called a reconfiguration sequence) 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.

本文言語English
ページ(範囲)111-122
ページ数12
ジャーナルTheoretical Computer Science
772
DOI
出版ステータスPublished - 2019 6 7

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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