The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs
Abstract
We study the problem of transforming one list (vertex) coloring of a graph into another list coloring by changing only one vertex color assignment at a time, while at all times maintaining a list coloring, given a list of allowed colors for each vertex. This problem is known to be PSPACE-complete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACE-complete even for bipartite series-parallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACE-completeness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomial-time algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives precise analyses of the problem with respect to pathwidth.
Keywords
Cite
@article{arxiv.1407.4235,
title = {The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs},
author = {Tatsuhiko Hatanaka and Takehiro Ito and Xiao Zhou},
journal= {arXiv preprint arXiv:1407.4235},
year = {2016}
}