Shortest reconfiguration of colorings under kempe changes

Marthe Bonamy, Takehiro Ito, Haruka Mizuta, Akira Suzuki, Marc Heinrich, Yusuke Kobayashi, Moritz Mühlenthaler, Kunihiro Wasa

研究成果: Conference contribution

抄録

A k-coloring of a graph maps each vertex of the graph to a color in {1, 2, . . ., k}, such that no two adjacent vertices receive the same color. Given a k-coloring of a graph, a Kempe change produces a new k-coloring by swapping the colors in a bicolored connected component. We investigate the complexity of finding the smallest number of Kempe changes needed to transform a given k-coloring into another given k-coloring. We show that this problem admits a polynomial-time dynamic programming algorithm on path graphs, which turns out to be highly non-trivial. Furthermore, the problem is NP-hard even on star graphs and we show that on such graphs it admits a constant-factor approximation algorithm and is fixed-parameter tractable when parameterized by the number k of colors. The hardness result as well as the algorithmic results are based on the notion of a canonical transformation.

本文言語English
ホスト出版物のタイトル37th International Symposium on Theoretical Aspects of Computer Science, STACS 2020
編集者Christophe Paul, Markus Blaser
出版社Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN(電子版)9783959771405
DOI
出版ステータスPublished - 2020 3
イベント37th International Symposium on Theoretical Aspects of Computer Science, STACS 2020 - Montpellier, France
継続期間: 2020 3 102020 3 13

出版物シリーズ

名前Leibniz International Proceedings in Informatics, LIPIcs
154
ISSN(印刷版)1868-8969

Conference

Conference37th International Symposium on Theoretical Aspects of Computer Science, STACS 2020
国/地域France
CityMontpellier
Period20/3/1020/3/13

ASJC Scopus subject areas

  • ソフトウェア

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