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

The tree-independence number tree- alpha $\text{tree\unicode{x02010}}\alpha $, first defined and studied by Dallard, Milani & ccaron;, and & Scaron;torgel, 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 ${\mathscr{C}}$ 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 ${\mathscr{C}}$ has bounded tree- alpha $\,\text{tree\unicode{x02010}}\,\alpha $. 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, Milani & ccaron;, and & Scaron;torgel that in a hereditary graph class, tree- alpha $\,\text{tree\unicode{x02010}}\,\alpha $ is bounded if and only if the treewidth is bounded by a function of the clique number.