Georgakopoulos coarse grid minor conjecture

Let $H$ be a planar graph. A graph is $H$-induced-minor-free if it does not contain $H$ as an induced minor, and a graph is $q$-quasi-isometric to a graph of treewidth at most $k$ if such a quasi-isometry exists with parameter $q$.

Georgakopoulos's coarse grid minor conjecture. For every planar graph $H$, there exist $k,q\in\mathbb{N}$ such that every $H$-induced-minor-free graph is $q$-quasi-isometric to a graph with treewidth at most $k$.

The conjecture is a coarse analogue of the grid-minor obstruction principle and is described as a major open problem in coarse graph theory. The paper notes that the original formulation uses forbidden fat-minors, which is more general than forbidden induced minors.