Abrishami, TaraAlecu, BogdanChudnovsky, MariaHajebi, SepehrSpirkl, SophieVuskovic, Kristina2024-05-012024-05-012024-04-24https://doi.org/10.1002/jgt.23104http://hdl.handle.net/10012/20528This 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.The 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.enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/algorithmic graph theoryeven-hole-free graphsstructural graph theorytree independence numbertreewidthArticle