English

The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs

Data Structures and Algorithms 2016-01-20 v1 Discrete Mathematics

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}
}
R2 v1 2026-06-22T05:05:11.076Z