Abu-Khzam, FN, Feghali, C and Muller, H (2015) Partitioning a graph into disjoint cliques and a triangle-free graph. Discrete Applied Mathematics, 190-19. 1 - 12. ISSN 0166-218X
Abstract
A graph G=(V,E) is partitionable if there exists a partition {A,B} of V such that A induces a disjoint union of cliques (i.e., G[A] is P_3-free) and B induces a triangle-free graph (i.e., G[B] is K_3-free). In this paper we investigate the computational complexity of deciding whether a graph is partitionable. The problem is known to be NP-complete on arbitrary graphs. Here it is proved that if a graph G is bull-free, planar, perfect, K_4-free or does not contain certain holes then deciding whether G is partitionable is NP-complete. This answers an open question posed by Thomassé, Trotignon and Vušković. In contrast a finite list of forbidden induced subgraphs is given for partitionable cographs.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Elsevier B.V. All rights reserved. This is an author produced version of a paper published in Discrete Applied Mathematics. Uploaded in accordance with the publisher's self-archiving policy |
Keywords: | computational complexity; graph partitioning; special graph class |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 19 Aug 2015 15:56 |
Last Modified: | 28 Apr 2016 16:56 |
Published Version: | http://dx.doi.org/10.1016/j.dam.2015.03.015 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.dam.2015.03.015 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:85292 |