Diameter of Colorings Under Kempe Changes

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

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

2 Citations (Scopus)

Abstract

Given a k-coloring of a graph G, a Kempe-change for two colors a and b produces another k-coloring of G, as follows: first choose a connected component in the subgraph of G induced by the two color classes of a and b, and then swap the colors a and b in the component. Two k-colorings are called Kempe-equivalent if one can be transformed into the other by a sequence of Kempe-changes. We consider two problems, defined as follows: First, given two k-colorings of a graph G, Kempe Reachability asks whether they are Kempe-equivalent; and second, given a graph G and a positive integer k, Kempe Connectivity asks whether any two k-colorings of G are Kempe-equivalent. We analyze the complexity of these problems from the viewpoint of graph classes. We prove that Kempe Reachability is PSPACE-complete for any fixed k ≥, and that it remains PSPACE-complete even when restricted to three colors and planar graphs of maximum degree six. Furthermore, we show that both problems admit polynomial-time algorithms on chordal graphs, bipartite graphs, and cographs. For each of these graph classes, we give a non-trivial upper bound on the number of Kempe-changes needed in order to certify that two k-colorings are Kempe-equivalent.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 25th International Conference, COCOON 2019, Proceedings
EditorsDing-Zhu Du, Zhenhua Duan, Cong Tian
PublisherSpringer Verlag
Pages52-64
Number of pages13
ISBN (Print)9783030261757
DOIs
Publication statusPublished - 2019
Event25th International Computing and Combinatorics Conference, COCOON 2019 - Xi'an, China
Duration: 2019 Jul 292019 Jul 31

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11653 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference25th International Computing and Combinatorics Conference, COCOON 2019
CountryChina
CityXi'an
Period19/7/2919/7/31

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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