Lokshtanov–McCarty bounded-degree region intersection conjecture

Let $H$ be a graph and let $\Delta\in\mathbb{N}$. A region intersection graph over a graph $H'$ is a graph whose vertices correspond to connected subgraphs of $H'$, with two vertices adjacent exactly when the corresponding subgraphs share a vertex.

Lokshtanov–McCarty's conjecture. There exists a graph $H'$ such that every $H$-induced-minor-free graph with maximum degree at most $\Delta$ is a region intersection graph over an $H'$-minor-free graph.

This is the bounded-degree version of a conjecture independently attributed to Lokshtanov and McCarty. The unrestricted conjecture was recently disproved, while the bounded-degree version is proposed in the source as an open revival.