Injective chromatic index of subcubic graphs

Prove that every subcubic graph has injective chromatic index at most 6.

Background

Injective edge-coloring assigns colors to edges so that any two edges having a common adjacent edge receive distinct colors. The injective chromatic index is the minimum number of colors required for such a coloring. For subcubic graphs, the paper reports an upper bound of 7 and formulates the stronger bound of 6 as a conjecture. The paper establishes bounds under additional maximum-average-degree or planarity restrictions, but does not resolve the conjecture for all subcubic graphs.