License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SWAT.2018.27
URN: urn:nbn:de:0030-drops-88539
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8853/
Ito, Takehiro ;
Otachi, Yota
Reconfiguration of Colorable Sets in Classes of Perfect Graphs
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.
BibTeX - Entry
@InProceedings{ito_et_al:LIPIcs:2018:8853,
author = {Takehiro Ito and Yota Otachi},
title = {{Reconfiguration of Colorable Sets in Classes of Perfect Graphs}},
booktitle = {16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
pages = {27:1--27:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-068-2},
ISSN = {1868-8969},
year = {2018},
volume = {101},
editor = {David Eppstein},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8853},
URN = {urn:nbn:de:0030-drops-88539},
doi = {10.4230/LIPIcs.SWAT.2018.27},
annote = {Keywords: reconfiguration, colorable set, perfect graph}
}
Keywords: |
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reconfiguration, colorable set, perfect graph |
Collection: |
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16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018) |
Issue Date: |
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2018 |
Date of publication: |
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04.06.2018 |