We show that for every positive integer t≥2 there exists an integer s such that every graph that contains no induced subgraph isomorphic to either the 6-vertex path or the (2,t)-biclique, the complete bipartite graph K2,t, has tree-independence number at most s. This result makes partial progress on a conjecture of Dallard, Krnc, Kwon, Milani\v{c}, Munaro, \v{S}torgel, and Wiederrecht.
@article{arxiv.2604.01999,
title = {Tree-independence number and forbidden induced subgraphs: excluding a $6$-vertex path and a $(2,t)$-biclique},
author = {Maria Chudnovsky and Julien Codsi and J. Pascal Gollin and Martin Milanič and Varun Sivashankar},
journal= {arXiv preprint arXiv:2604.01999},
year = {2026}
}