Planar D-chromatic index conjecture

Let $G$ be a planar graph with maximum degree $\Delta\ge 4$, and let $\chi'_D(G)$ denote the minimum number of colors in a proper edge coloring in which every diamond subgraph is rainbow.

Planar D-chromatic index conjecture. For every such graph,

$$\chi'_D(G)\le\begin{cases} 9 &\text{if } \Delta=4, \\ 10 &\text{if } \Delta=5, \\ 2\Delta-1 &\text{if } \Delta\ge 6. \end{cases}$$

This conjecture concerns the sharper planar bounds not established by the results stated in the provided text; the text gives the general planar bound $\chi'_D(G)\le 2\Delta$ for $\Delta\ge 38$.