Parameterized complexity of the list coloring reconfiguration problem with graph parameters

Tatsuhiko Hatanaka, Takehiro Ito, Xiao Zhou

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

2 Citations (Scopus)

Abstract

Let G be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. For two given list colorings of G, we study the problem of transforming one into the other by changing only one vertex color assignment at a time, while at all times maintaining a list coloring. This problem is known to be PSPACEcomplete even for bounded bandwidth graphs and a fixed constant k. In this paper, we study the fixed-parameter tractability of the problem when parameterized by several graph parameters. We first give a fixed-parameter algorithm for the problem when parameterized by k and the modular-width of an input graph. We next give a fixed-parameter algorithm for the shortest variant which computes the length of a shortest transformation when parameterized by k and the size of a minimum vertex cover of an input graph. As corollaries, we show that the problem for cographs and the shortest variant for split graphs are fixed-parameter tractable even when only k is taken as a parameter. On the other hand, we prove that the problem is W[1]-hard when parameterized only by the size of a minimum vertex cover of an input graph.

Original languageEnglish
Title of host publication42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
EditorsKim G. Larsen, Jean-Francois Raskin, Hans L. Bodlaender
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770460
DOIs
Publication statusPublished - 2017 Nov 1
Event42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 - Aalborg, Denmark
Duration: 2017 Aug 212017 Aug 25

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume83
ISSN (Print)1868-8969

Other

Other42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
CountryDenmark
CityAalborg
Period17/8/2117/8/25

Keywords

  • Combinatorial reconfiguration
  • Fixed-parameter tractability
  • Graph algorithm
  • List coloring
  • W[1]-hardness

ASJC Scopus subject areas

  • Software

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