Abrishami, T., Chudnovsky, M., Dibek, C. et al. (3 more authors) (2022) Graphs with polynomially many minimal separators. Journal of Combinatorial Theory, Series B, 152. pp. 248-280. ISSN 0095-8956
Abstract
We show that graphs that do not contain a theta, pyramid, prism, or turtle as an induced subgraph have polynomially many minimal separators. This result is the best possible in the sense that there are graphs with exponentially many minimal separators if only three of the four induced subgraphs are excluded. As a consequence, there is a polynomial time algorithm to solve the maximum weight independent set problem for the class of (theta, pyramid, prism, turtle)-free graphs. Since every prism, theta, and turtle contains an even hole, this also implies a polynomial time algorithm to solve the maximum weight independent set problem for the class of (pyramid, even hole)-free graphs.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Elsevier Inc. All rights reserved. This is an author produced version of an article published in Journal of Combinatorial Theory, Series B made available under the CC-BY-NC-ND 4.0 license (http://creativecommons.org/licenses/by-nc-nd/4.0) in accordance with the publisher's self-archiving policy. |
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: | 16 Jan 2024 16:17 |
Last Modified: | 27 Jul 2024 04:31 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jctb.2021.10.003 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:207735 |