2026-07-23T07:14:27Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8853 2024-03-06T10:42:48Z ddc:004 open_access

Reconfiguration of Colorable Sets in Classes of Perfect Graphs Ito, Takehiro Otachi, Yota reconfiguration colorable set perfect graph 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Takehiro Ito and Yota Otachi 2018 Is Part Of LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SWAT.2018.27 urn:nbn:de:0030-drops-88539 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.27 eng https://creativecommons.org/licenses/by/3.0/legalcode