Hudák–Lużar–Soták–Škrekovski planar strong edge-coloring conjecture

Let $G$ be a planar graph of girth $g\ge5$ and maximum degree $\Delta$. Hudák–Lużar–Soták–Škrekovski conjecture. There exists a constant $C$ such that

$$\chi^s(G)\le\left\lceil\frac{2g(\Delta-1)}{g-1}\right\rceil+C.$$

The conjecture proposes that the pendant-edge construction described in the survey is extremal up to an additive constant. The survey records partial progress but no resolution.