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Tree independence number I. (Even hole, diamond, pyramid)-free graphs

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dc.contributor.authorAbrishami, Tara
dc.contributor.authorAlecu, Bogdan
dc.contributor.authorChudnovsky, Maria
dc.contributor.authorHajebi, Sepehr
dc.contributor.authorSpirkl, Sophie
dc.contributor.authorVuskovic, Kristina
dc.date.accessioned2024-05-01T15:11:21Z
dc.date.available2024-05-01T15:11:21Z
dc.date.issued2024-04-24
dc.descriptionThis is an open access article under the terms of the Creative Commons Attribution License https://creativecommons.org/licenses/by/4.0/, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2024 The Authors. Journal of Graph Theory published by Wiley Periodicals LLC.en
dc.description.abstractThe tree‐independence number tree‐α, first defined and studied by Dallard, Milanič, and Štorgel, is a variant of treewidth tailored to solving the maximum independent set problem. Over a series of papers, Abrishami et al. developed the so‐called central bag method to study induced obstructions to bounded treewidth. Among others, they showed that, in a certain superclass C of (even hole, diamond, pyramid)‐free graphs, treewidth is bounded by a function of the clique number. In this paper, we relax the bounded clique number assumption, and show that C has bounded tree‐α. Via existing results, this yields a polynomial‐time algorithm for the Maximum Weight Independent Set problem in this class. Our result also corroborates, for this class of graphs, a conjecture of Dallard, Milanič, and Štorgel that in a hereditary graph class, tree‐α is bounded if and only if the treewidth is bounded by a function of the clique number.en
dc.description.sponsorshipGovernment of Ontario || Air Force Office of Scientific Research || Natural Sciences and Engineering Research Council of Canada || Alexander von Humboldt-Stuftung || Division of Mathematical Sciences || National Science Foundation || Engineering and Physical Sciences Research Council.en
dc.identifier.urihttps://doi.org/10.1002/jgt.23104
dc.identifier.urihttp://hdl.handle.net/10012/20528
dc.language.isoenen
dc.publisherWileyen
dc.relation.ispartofseriesJournal of Graph Theory;
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectalgorithmic graph theoryen
dc.subjecteven-hole-free graphsen
dc.subjectstructural graph theoryen
dc.subjecttree independence numberen
dc.subjecttreewidthen
dc.titleTree independence number I. (Even hole, diamond, pyramid)-free graphsen
dc.typeArticleen
dcterms.bibliographicCitationAbrishami, T., Alecu, B., Chudnovsky, M., Hajebi, S., Spirkl, S., & Vušković, K. (2024). Tree Independence Number I. (even Hole, Diamond, Pyramid)‐free graphs. Journal of Graph Theory. https://doi.org/10.1002/jgt.23104en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen
uws.typeOfResourceTexten

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