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The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs
Tatsuhiko HATANAKA Takehiro ITO Xiao ZHOU
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E98A
No.6
pp.11681178 Publication Date: 2015/06/01 Online ISSN: 17451337
DOI: 10.1587/transfun.E98.A.1168 Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications) Category: Keyword: graph algorithm, list coloring, pathwidth, PSPACEcomplete, reachability on solution space, reconfiguration,
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Summary:
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 PSPACEcomplete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACEcomplete even for bipartite seriesparallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACEcompleteness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomialtime algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives sharp analyses of the problem with respect to pathwidth.

