eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-12-06
37:1
37:13
10.4230/LIPIcs.ISAAC.2018.37
article
Algorithms for Coloring Reconfiguration Under Recolorability Constraints
Osawa, Hiroki
1
Suzuki, Akira
1
https://orcid.org/0000-0002-5212-0202
Ito, Takehiro
1
https://orcid.org/0000-0002-9912-6898
Zhou, Xiao
1
Graduate School of Information Sciences, Tohoku University, Japan
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol123-isaac2018/LIPIcs.ISAAC.2018.37/LIPIcs.ISAAC.2018.37.pdf
combinatorial reconfiguration
graph algorithm
graph coloring