Petruševski–Škrekovski conjecture on odd colorings of planar graphs

Let $G$ be a planar graph. An odd coloring of $G$ is a proper vertex coloring such that every non-isolated vertex has a color appearing an odd number of times in its neighborhood; let $\chi_o(G)$ be the minimum number of colors in such a coloring. Petruševski–Škrekovski conjecture. For every planar graph $G$,

$$\chi_o(G)\leq 5.$$

Petruševski and Škrekovski introduced odd coloring and proved that every planar graph is odd 9-colorable. The conjectured bound 5 remains open.