The Coloring Reconfiguration Problem on Specific Graph Classes

Abstract

We study the problem of transforming one (vertex) k-coloring of a graph into another one by changing only one vertex color assignment at a time, while at all times maintaining a k-coloring, where k denotes the number of colors. This decision problem is known to be PSPACE-complete even for bipartite graphs and any fixed constant \(k \ge 4\). In this paper, we study the problem from the viewpoint of graph classes. We first show that the problem remains PSPACE-complete for chordal graphs even if the number of colors is a fixed constant. We then demonstrate that, even when the number of colors is a part of input, the problem is solvable in polynomial time for several graph classes, such as split graphs and trivially perfect graphs.