The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs

Tatsuhiko HATANAKA  Takehiro ITO  Xiao ZHOU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E98-A   No.6   pp.1168-1178
Publication Date: 2015/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E98.A.1168
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
graph algorithm,  list coloring,  pathwidth,  PSPACE-complete,  reachability on solution space,  reconfiguration,  

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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 sharp analyses of the problem with respect to pathwidth.