Tree independence number I. (Even hole, diamond, pyramid)-free graphs
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Date
2024-04-24
Authors
Abrishami, Tara
Alecu, Bogdan
Chudnovsky, Maria
Hajebi, Sepehr
Spirkl, Sophie
Vuskovic, Kristina
Journal Title
Journal ISSN
Volume Title
Publisher
Wiley
Abstract
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.
Description
This 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.
Keywords
algorithmic graph theory, even-hole-free graphs, structural graph theory, tree independence number, treewidth