Alon–Tarsi bound for vertex-face graphs of plane graphs

Let $G$ be a plane graph, and let $G_{vf}$ denote its vertex-face graph. The Alon–Tarsi conjecture. Every plane graph $G$ satisfies

$$\operatorname{AT}(G_{vf})\leqslant 7.$$

This would extend the corresponding list-colouring bound, whose optimality is unknown; the authors explain that proving non-vanishing of the relevant graph-polynomial monomial would establish the claim.