Tree-independence number and forbidden induced subgraphs: excluding a $6$-vertex path and a $(2,t)$-biclique

Abstract

We show that for every positive integer ${t \geq 2}$ 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 $K_{2,t}$, 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.