Neumann–Lara–Škrekovski conjecture on the dichromatic number of planar graphs

Let $G$ be a planar graph, and let $\vec{\chi}(G)$ denote the maximum, over all orientations of $G$, of the minimum number of acyclic colour classes in a vertex colouring. Neumann–Lara–Škrekovski conjecture. Every planar graph satisfies

$$\vec{\chi}(G) \leq 2.$$

This is the directed analogue of the Four-Colour Theorem and is equivalent, as stated in the source, to the assertion that every planar digraph is $2$-colourable. The source does not provide evidence of a resolution.