Mácajová–Raspaud–Škoviéra signed Four Color conjecture

All graphs are finite, simple, undirected graphs. Let $G$ be a graph and let $\sigma:E(G)\to\{-1,+1\}$ be a signature; the pair $(G,\sigma)$ is a signed graph, with underlying graph $G$. A $k$-signed coloring of $(G,\sigma)$ uses the $k$ colors specified according to the parity of $k$, and assigns colors so that for every edge $e=uv$, $c(u)\ne\sigma(e)\cdot c(v)$. Write $\chi(G)$ for the least $k$ admitting such a coloring. Mácajová–Raspaud–Škoviéra's conjecture. If $G$ is a simple signed planar graph, then

$$\chi(G)\le 4.$$

This is the signed-graph analogue of the Four Color Theorem: it asserts that every simple signed planar graph admits a signed coloring with at most four colors. The source attributes the conjecture to Mácajová, Raspaud and Škoviéra; its resolution is not established by the supplied context.