Radovanović, M, Trotignon, N and Vušković, K (2020) The (theta, wheel)-free graphs Part III: Cliques, stable sets and coloring. Journal of Combinatorial Theory, Series B, 143. pp. 185-218. ISSN 0095-8956
Abstract
A hole in a graph is a chordless cycle of length at least 4. A theta is a graph formed by three paths between the same pair of distinct vertices so that the union of any two of the paths induces a hole. A wheel is a graph formed by a hole and a vertex that has at least 3 neighbors in the hole. In this series of papers we study the class of graphs that do not contain as an induced subgraph a theta nor a wheel. In Part II of the series we prove a decomposition theorem for this class, that uses clique cutsets and 2-joins, and consequently obtain a polynomial time recognition algorithm for the class. In this paper we further use this decomposition theorem to obtain polynomial time algorithms for maximum weight clique, maximum weight stable set and coloring problems. We also show that for a graph G in the class, if its maximum clique size is ω, then its chromatic number is bounded by max{w,3}, and that the class is 3-clique-colorable.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Crown Copyright © 2019 Published by Elsevier Inc. All rights reserved. This is an author produced version of an article published in Journal of Combinatorial Theory, Series B. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Wheel; Theta; Truemper configuration; Algorithm; Clique; Stable set; Vertex-coloring; Clique-coloring |
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) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/N019660/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 08 May 2019 15:48 |
Last Modified: | 17 Jul 2020 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jctb.2019.07.003 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:145753 |