Dvořák–Mohar–Šámal's subcubic star chromatic index conjecture

Let $G$ be a subcubic graph. The Dvořák–Mohar–Šámal conjecture.

$$\chi_{\mathrm{star}}'(G) \leq 6.$$

The star chromatic index is the minimum number of colors in a star edge-coloring, in which every bichromatic subgraph contains no path or cycle of length four. The conjecture improves the known upper bound $\chi_{\mathrm{star}}'(G)\leq 7$ for subcubic graphs and remains open.