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DOI: 10.4230/LIPIcs.MFCS.2017.51
URN: urn:nbn:de:0030-drops-81060
URL: http://drops.dagstuhl.de/opus/volltexte/2017/8106/
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Hatanaka, Tatsuhiko ; Ito, Takehiro ; Zhou, Xiao

Parameterized Complexity of the List Coloring Reconfiguration Problem with Graph Parameters

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LIPIcs-MFCS-2017-51.pdf (3 MB)


Abstract

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.

BibTeX - Entry

@InProceedings{hatanaka_et_al:LIPIcs:2017:8106,
  author =	{Tatsuhiko Hatanaka and Takehiro Ito and Xiao Zhou},
  title =	{{Parameterized Complexity of the List Coloring Reconfiguration Problem with Graph Parameters}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{51:1--51:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8106},
  URN =		{urn:nbn:de:0030-drops-81060},
  doi =		{10.4230/LIPIcs.MFCS.2017.51},
  annote =	{Keywords: combinatorial reconfiguration, fixed-parameter tractability, graph algorithm, list coloring, W[1]-hardness}
}

Keywords: combinatorial reconfiguration, fixed-parameter tractability, graph algorithm, list coloring, W[1]-hardness
Seminar: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Issue Date: 2017
Date of publication: 22.11.2017


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