K.K. Dabrowski
On colouring (2P2,H)-free and (P5,H)-free graphs
Dabrowski, K.K.; Paulusma, D.
Abstract
The Colouring problem asks whether the vertices of a graph can be coloured with at most k colours for a given integer k in such a way that no two adjacent vertices receive the same colour. A graph is (H1,H2)-free if it has no induced subgraph isomorphic to H1 or H2. A connected graph H1 is almost classified if Colouring on (H1,H2)-free graphs is known to be polynomial-time solvable or NP-complete for all but finitely many connected graphs H2. We show that every connected graph H1 apart from the claw K1,3 and the 5-vertex path P5 is almost classified. We also prove a number of new hardness results for Colouring on (2P2,H)-free graphs. This enables us to list all graphs H for which the complexity of Colouring is open on (2P2,H)-free graphs and all graphs H for which the complexity of Colouring is open on (P5,H)-free graphs. In fact we show that these two lists coincide. Moreover, we show that the complexities of Colouring for (2P2,H)-free graphs and for (P5,H)-free graphs are the same for all known cases.
Citation
Dabrowski, K., & Paulusma, D. (2018). On colouring (2P2,H)-free and (P5,H)-free graphs. Information Processing Letters, 134, 35-41. https://doi.org/10.1016/j.ipl.2018.02.003
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 2, 2018 |
Online Publication Date | Feb 5, 2018 |
Publication Date | Jun 1, 2018 |
Deposit Date | Feb 5, 2018 |
Publicly Available Date | Feb 6, 2018 |
Journal | Information Processing Letters |
Print ISSN | 0020-0190 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 134 |
Pages | 35-41 |
DOI | https://doi.org/10.1016/j.ipl.2018.02.003 |
Public URL | https://durham-repository.worktribe.com/output/1335526 |
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
Copyright Statement
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Published Journal Article
(378 Kb)
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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/
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