The bounded-degree fat-grid tree-width conjecture

Let $K,d,n\in\mathbb{N}$. A graph has a $K$-fat $(n\times n)$-grid minor when it contains the corresponding fat minor model. Then there exists some $g\in\mathbb{N}$ such that every graph with maximum degree at most $d$ and with no $K$-fat $(n\times n)$-grid minor has tree-width at most $g$. Bounded-degree fat-grid tree-width conjecture.

This is a proposed strengthening of the bounded-degree induced-minor result. The paper does not establish it; its status is open in the supplied text.