Fiorini–Huynh–Joret–Pashkovich conjecture on spanning tree polytopes in minor-closed classes

Let $\mathcal{G}$ be a proper minor-closed graph class, and let $G$ be a connected $n$-vertex graph in $\mathcal{G}$. The spanning tree polytope of $G$ is the convex hull of the incidence vectors of its spanning trees. Fiorini–Huynh–Joret–Pashkovich conjecture. The spanning tree polytope of every connected $n$-vertex graph in $\mathcal{G}$ has extension complexity in $O(n)$. This would improve the paper's $O(n^{3/2})$ bound for every proper minor-closed graph class and would establish linear-size extended formulations throughout these classes.