2026-07-22T06:50:14Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8258 2024-03-06T10:41:53Z ddc:004 open_access

Complexity of Coloring Reconfiguration under Recolorability Constraints Osawa, Hiroki Suzuki, Akira Ito, Takehiro Zhou, Xiao combinatorial reconfiguration graph coloring PSPACE-complete 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hiroki Osawa and Akira Suzuki and Takehiro Ito and Xiao Zhou 2017 Is Part Of LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2017.62 urn:nbn:de:0030-drops-82588 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.62 eng https://creativecommons.org/licenses/by/3.0/legalcode