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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 15:11:21 (GMT) 15:11:21 (GMT)
dc.descriptionThis is an open access article under the terms of the Creative Commons Attribution License, 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.relation.ispartofseriesJournal of Graph Theory;
dc.rightsAttribution 4.0 International*
dc.subjectalgorithmic graph theoryen
dc.subjecteven-hole-free graphsen
dc.subjectstructural graph theoryen
dc.subjecttree independence numberen
dc.titleTree independence number I. (Even hole, diamond, pyramid)-free graphsen
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.
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen

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