License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SWAT.2016.16
URN: urn:nbn:de:0030-drops-60380
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6038/
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Dabrowski, Konrad K. ; Dross, François ; Paulusma, Daniël

Colouring Diamond-free Graphs

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LIPIcs-SWAT-2016-16.pdf (0.5 MB)

Abstract

The Colouring problem is that of deciding, given a graph G and an integer k, whether G admits a (proper) k-colouring. For all graphs H up to five vertices, we classify the computational complexity of Colouring for (diamond,H)-free graphs. Our proof is based on combining known results together with proving that the clique-width is bounded for (diamond,P_1+2P_2)-free graphs. Our technique for handling this case is to reduce the graph under consideration to a k-partite graph that has a very specific decomposition. As a by-product of this general technique we are also able to prove boundedness of clique-width for four other new classes of (H_1,H_2)-free graphs. As such, our work also continues a recent systematic study into the (un)boundedness of clique-width of (H_1,H_2)-free graphs, and our five new classes of bounded clique-width reduce the number of open cases from 13 to 8.

BibTeX - Entry

@InProceedings{dabrowski_et_al:LIPIcs:2016:6038,
  author =	{Konrad K. Dabrowski and Fran{\c{c}}ois Dross and Dani{\"e}l Paulusma},
  title =	{{Colouring Diamond-free Graphs}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{16:1--16:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Rasmus Pagh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6038},
  URN =		{urn:nbn:de:0030-drops-60380},
  doi =		{10.4230/LIPIcs.SWAT.2016.16},
  annote =	{Keywords: colouring, clique-width, diamond-free, graph class, hereditary graph class}
}

Keywords: colouring, clique-width, diamond-free, graph class, hereditary graph class
Collection: 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)
Issue Date: 2016
Date of publication: 22.06.2016

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