TY - JOUR

T1 - The list coloring reconfiguration problem for bounded pathwidth graphs

AU - Hatanaka, Tatsuhiko

AU - Ito, Takehiro

AU - Zhou, Xiao

PY - 2015/6/1

Y1 - 2015/6/1

N2 - 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 seriesparallel 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.

AB - 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 seriesparallel 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.

KW - Graph algorithm

KW - List coloring

KW - PSPACE-complete

KW - Pathwidth

KW - Reachability on solution space

KW - Reconfiguration

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U2 - 10.1587/transfun.E98.A.1168

DO - 10.1587/transfun.E98.A.1168

M3 - Article

AN - SCOPUS:84930427944

VL - E98A

SP - 1168

EP - 1178

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 6

ER -