Tree independence number III. Thetas, prisms and stars

TL;DR

This paper establishes a bound on the tree independence number for graphs excluding certain subgraphs, specifically theta, prism, and star structures, demonstrating a unifying property across these classes.

Contribution

It proves that for any fixed t, there exists a universal bound on the tree independence number for graphs free of theta, prism, and star subgraphs.

Findings

Bound on tree independence number for (theta, prism, K_{1,t})-free graphs

Unification of structural graph properties

Extension of previous results to broader graph classes

Abstract

We prove that for every $t\in \mathbb{N}$, there exists $\tau=\tau(t)\in \mathbb{N}$ such that every (theta, prism, $K_{1,t}$)-free graph has tree independence number at most $\tau$ (where we allow "prisms" to have one path of length zero).