Shortest reconfiguration of colorings under kempe changes

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publication37th International Symposium on Theoretical Aspects of Computer Science, STACS 2020
EditorsChristophe Paul, Markus Blaser
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771405
DOIs
Publication statusPublished - 2020 Mar
Event37th International Symposium on Theoretical Aspects of Computer Science, STACS 2020 - Montpellier, France
Duration: 2020 Mar 102020 Mar 13

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume154
ISSN (Print)1868-8969

Conference

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

Keywords

  • Combinatorial Reconfiguration
  • Graph Algorithms
  • Graph Coloring
  • Kempe Equivalence

ASJC Scopus subject areas

  • Software

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