Complexity of Coloring Reconfiguration under Recolorability Constraints

Authors Hiroki Osawa, Akira Suzuki, Takehiro Ito, Xiao Zhou

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Hiroki Osawa
Akira Suzuki
Takehiro Ito
Xiao Zhou

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Hiroki Osawa, Akira Suzuki, Takehiro Ito, and Xiao Zhou. Complexity of Coloring Reconfiguration under Recolorability Constraints. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 62:1-62:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


For an integer k \ge 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 \ge 4, and solvable for any graph in polynomial time if k \le 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.
  • combinatorial reconfiguration
  • graph coloring
  • PSPACE-complete


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