eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-01
51:1
51:13
10.4230/LIPIcs.MFCS.2017.51
article
Parameterized Complexity of the List Coloring Reconfiguration Problem with Graph Parameters
Hatanaka, Tatsuhiko
Ito, Takehiro
Zhou, Xiao
Let G be a graph such that each vertex has its list of available colors, and assume that each list is a subset of the common set consisting of k colors. For two given list colorings of G, we study the problem of transforming one into the other by changing only one vertex color assignment at a time, while at all times maintaining a list coloring. This problem is known to be PSPACE-complete even for bounded bandwidth graphs and a fixed constant k. In this paper, we study the fixed-parameter tractability of the problem when parameterized by several graph parameters. We first give a fixed-parameter algorithm for the problem when parameterized by k and the modular-width of an input graph. We next give a fixed-parameter algorithm for the shortest variant which computes the length of a shortest transformation when parameterized by k and the size of a minimum vertex cover of an input graph. As corollaries, we show that the problem for cographs and the shortest variant for split graphs are fixed-parameter tractable even when only k is taken as a parameter. On the other hand, we prove that the problem is W[1]-hard when parameterized only by the size of a minimum vertex cover of an input graph.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol083-mfcs2017/LIPIcs.MFCS.2017.51/LIPIcs.MFCS.2017.51.pdf
combinatorial reconfiguration
fixed-parameter tractability
graph algorithm
list coloring
W[1]-hardness