TY - GEN

T1 - Parameterized complexity of the list coloring reconfiguration problem with graph parameters

AU - Hatanaka, Tatsuhiko

AU - Ito, Takehiro

AU - Zhou, Xiao

N1 - Funding Information:
∗ This work is partially supported by JST CREST Grant Number JPMJCR1402, and by JSPS KAKENHI Grant Numbers JP16J02175, JP16K00003, and JP16K00004. † A full version of the paper is available at https://arxiv.org/abs/1705.07551.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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 PSPACEcomplete 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.

AB - 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 PSPACEcomplete 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.

KW - Combinatorial reconfiguration

KW - Fixed-parameter tractability

KW - Graph algorithm

KW - List coloring

KW - W[1]-hardness

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UR - http://www.scopus.com/inward/citedby.url?scp=85038428852&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.MFCS.2017.51

DO - 10.4230/LIPIcs.MFCS.2017.51

M3 - Conference contribution

AN - SCOPUS:85038428852

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017

A2 - Larsen, Kim G.

A2 - Raskin, Jean-Francois

A2 - Bodlaender, Hans L.

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017

Y2 - 21 August 2017 through 25 August 2017

ER -