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DOI: 10.4230/LIPIcs.SWAT.2016.16
URN: urn:nbn:de:0030-drops-60380
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6038/
Dabrowski, Konrad K. ; Dross, François ; Paulusma, Daniël
Colouring Diamond-free Graphs
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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 | |
| Seminar: | 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016) | |
| Issue date: | 2016 | |
| Date of publication: | 22.06.2016 |
