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DOI: 10.4230/LIPIcs.ISAAC.2018.5
URN: urn:nbn:de:0030-drops-99533
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9953/
Klimosová, Tereza ; Malík, Josef ; Masarík, Tomás ; Novotná, Jana ; Paulusma, Daniël ; Slívová, Veronika
Colouring (P_r+P_s)-Free Graphs
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Abstract
The k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer k such that no two adjacent vertices are coloured alike. If each vertex u must be assigned a colour from a prescribed list L(u) subseteq {1,...,k}, then we obtain the List k-Colouring problem. A graph G is H-free if G does not contain H as an induced subgraph. We continue an extensive study into the complexity of these two problems for H-free graphs. We prove that List 3-Colouring is polynomial-time solvable for (P_2+P_5)-free graphs and for (P_3+P_4)-free graphs. Combining our results with known results yields complete complexity classifications of 3-Colouring and List 3-Colouring on H-free graphs for all graphs H up to seven vertices. We also prove that 5-Colouring is NP-complete for (P_3+P_5)-free graphs.
BibTeX - Entry
@InProceedings{klimosov_et_al:LIPIcs:2018:9953,
author = {Tereza Klimosov{\'a} and Josef Mal{\'i}k and Tom{\'a}s Masar{\'i}k and Jana Novotn{\'a} and Dani{\"e}l Paulusma and Veronika Sl{\'i}vov{\'a}},
title = {{Colouring (P_r+P_s)-Free Graphs}},
booktitle = {29th International Symposium on Algorithms and Computation (ISAAC 2018)},
pages = {5:1--5:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-094-1},
ISSN = {1868-8969},
year = {2018},
volume = {123},
editor = {Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9953},
URN = {urn:nbn:de:0030-drops-99533},
doi = {10.4230/LIPIcs.ISAAC.2018.5},
annote = {Keywords: vertex colouring, H-free graph, linear forest}
}
| Keywords: | vertex colouring, H-free graph, linear forest | |
| Seminar: | 29th International Symposium on Algorithms and Computation (ISAAC 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 06.12.2018 |
