Exponential 3-arboral coloring conjecture for toroidal graphs

Let $G$ be a graph embeddable in the torus. An arboreal 3-coloring of $G$ is a coloring with three colors such that each color class induces a forest. Exponential 3-arboral coloring conjecture. There exists an edge $e\in E(G)$ such that $G-e$ has exponentially many arboreal 3-colorings. The paper observes that every toroidal graph has an edge whose deletion leaves a graph of vertex-arboricity at most $3$, and conjectures that one such deletion always yields exponentially many 3-arboral colorings. The conjecture is presented without a resolution in the paper.