Conjecture on the proper open conflict-free chromatic index

Let $G$ be a graph with maximum degree $\Delta$, and let $\chi_{\rm pOCF}'(G)$ denote its proper open conflict-free chromatic index.

Proper open conflict-free chromatic-index conjecture. For every graph $G$ with maximum degree $\Delta$,

$$\chi_{\rm pOCF}'(G)\leq \Delta+3.$$

The conjecture aims to improve the currently available general upper bound, which is slightly above $2\Delta$, to within an absolute constant of the trivial lower bound $\Delta$.