Dvořák et al.'s star chromatic index conjecture for subcubic graphs

Let $G$ be a subcubic graph, meaning that every vertex of $G$ has degree at most $3$, and let $\chi'_{st}(G)$ denote the minimum number of colors in a proper edge-coloring of $G$ with no bichromatic path or cycle of length four. Dvořák et al.'s conjecture.

$$\chi'_{st}(G) \leq 6.$$

Although the conjecture remains open, it has been confirmed for special classes including subcubic outer-planar graphs and subcubic graphs with maximum average degree at most $5/2$.