The general sparse induced-subgraph conjecture

Let $\operatorname{tw}(G)$ denote the treewidth of $G$. The general sparse induced-subgraph conjecture. For every $t\geq 1$, every graph of sufficiently large treewidth has an induced subgraph of treewidth $t$ which is either complete or $K_4$-free. The source presents this as a possible extension beyond even-hole-free graphs, motivated by known sparse obstructions; no resolution is given.