D-coloring of planar graphs

A proper edge-coloring of a graph $G$ is a D-coloring if every subgraph isomorphic to $K_4-e$ is rainbow. The minimum number of colors in such a coloring is the D-chromatic index $\chi'_D(G)$. Wang conjectured that every planar graph of maximum degree $\Delta \ge 4$ satisfies $\chi'_D(G) \le 9$ for $\Delta = 4$, $\chi'_D(G) \le 10$ for $\Delta = 5$, and $\chi'_D(G) \le 2\Delta - 1$ for $\Delta \ge 6$. We prove that every planar graph $G$ satisfies $$\chi_D'(G) \leq \begin{cases} 9, & \Delta(G) \leq 4, \\ 10, & \Delta(G) = 5, \\ 2\Delta(G) - 1, & \Delta(G) \geq 33. \end{cases}$$ Each bound is best possible in its stated range. Consequently, Wang's conjecture remains open only for $6 \le \Delta \le 32$.