Algorithms for coloring reconfiguration under recolorability constraints

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

Abstract

Coloring reconfiguration is one of the most well-studied reconfiguration problems. In the problem, we are given two (vertex-)colorings of a graph using at most k colors, and asked to determine whether there exists a transformation between them by recoloring only a single vertex at a time, while maintaining a k-coloring throughout. It is known that this problem is solvable in linear time for any graph if k ≤ 3, while is PSPACE-complete for a fixed k ≥ 4. In this paper, we further investigate the problem from the viewpoint of recolorability constraints, which forbid some pairs of colors to be recolored directly. More specifically, the recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color, and each edge in R represents a pair of colors that can be recolored directly. In this paper, we give a linear-time algorithm to solve the problem under such a recolorability constraint if R is of maximum degree at most two. In addition, we show that the minimum number of recoloring steps required for a desired transformation can be computed in linear time for a yes-instance. We note that our results generalize the known positive ones for coloring reconfiguration.

Original languageEnglish
Title of host publication29th International Symposium on Algorithms and Computation, ISAAC 2018
EditorsWen-Lian Hsu, Der-Tsai Lee, Chung-Shou Liao
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages37:1-37:13
ISBN (Electronic)9783959770941
DOIs
Publication statusPublished - 2018 Dec 1
Event29th International Symposium on Algorithms and Computation, ISAAC 2018 - Jiaoxi, Yilan, Taiwan, Province of China
Duration: 2018 Dec 162018 Dec 19

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume123
ISSN (Print)1868-8969

Conference

Conference29th International Symposium on Algorithms and Computation, ISAAC 2018
CountryTaiwan, Province of China
CityJiaoxi, Yilan
Period18/12/1618/12/19

Keywords

  • And phrases combinatorial reconfiguration
  • Graph algorithm
  • Graph coloring

ASJC Scopus subject areas

  • Software

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