Complexity of coloring reconfiguration under recolorability constraints

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For an integer k 1, k-coloring reconfiguration is one of the most well-studied reconfiguration problems, defined as follows: In the problem, we are given two (vertex)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper coloring. The problem is known to be PSPACE-complete if k 4, and solvable for any graph in polynomial time if k 3. In this paper, we introduce a recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. 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. We study the hardness of the problem based on the structure of recolorability constraints R. More specifically, we prove that the problem is PSPACE-complete if R is of maximum degree at least four, or has a connected component containing more than one cycle.

Original languageEnglish
Title of host publication28th International Symposium on Algorithms and Computation, ISAAC 2017
EditorsTakeshi Tokuyama, Yoshio Okamoto
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770545
Publication statusPublished - 2017 Dec 1
Event28th International Symposium on Algorithms and Computation, ISAAC 2017 - Phuket, Thailand
Duration: 2017 Dec 92017 Dec 22

Publication series

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


Conference28th International Symposium on Algorithms and Computation, ISAAC 2017


  • Combinatorial reconfiguration
  • Graph coloring
  • Pspace-complete


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