### 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 |
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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 18 → 2018 6 20 |

### 出版物シリーズ

名前 | Leibniz International Proceedings in Informatics, LIPIcs |
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巻 | 101 |

ISSN（印刷物） | 1868-8969 |

### Other

Other | 16th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2018 |
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国 | Sweden |

市 | Malmo |

期間 | 18/6/18 → 18/6/20 |

### ASJC Scopus subject areas

- Software

## フィンガープリント Reconfiguration of colorable sets in classes of perfect graphs' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

## これを引用

*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