Wang–Lih planar high-girth square-coloring conjecture

Let $G$ be a planar graph of girth at least $k$, and let $\Delta$ be its maximum degree. Wang–Lih conjecture. For every $k\ge 5$, there exists $\Delta_k$ such that, if $\Delta\ge\Delta_k$, then

$$\chi^2(G)=\Delta+1.$$

The conjecture asks whether the trivial lower bound is asymptotically exact for planar graphs of every fixed girth at least five; the survey later states that it has been completely resolved.