Lai et al.'s conjecture on dynamic coloring of planar graphs

Let $G$ be a planar graph and let $r$ be a positive integer. The $r$-dynamic chromatic number $\chi_r^d(G)$ is the least number of colors in an $r$-dynamic proper coloring of $G$.

Lai et al.'s conjecture.

$$\chi_r^d(G)\leq\left\{ \begin{array}{lcl} r+3, && {if\ 1\leq r\leq2;}\\ r+5, &&{if\ 3\leq r\leq7;}\\ \lfloor\frac{3r}{2}\rfloor+1, &&{if\ r\geq8.} \end{array}\right.$$

This is presented as a conjecture about dynamic coloring of planar graphs, analogous to Wegner's conjecture. The supplied text does not state whether it has been resolved.