Brešar–Togni conjecture on packing coloring of subdivided subcubic graphs

Let $G$ be a graph in which every vertex has degree at most $3$, and let $S(G)$ be the graph obtained by subdividing every edge of $G$, replacing each edge $uv$ by a path $u$-$w$-$v$ through a new vertex $w$. Brešar–Togni conjecture. Every subcubic graph satisfies

$$\chi_p(S(G))\leq 5.$$

This conjecture asks for a universal upper bound on the packing chromatic number of the subdivision of a subcubic graph. It arose from work of Gastineau and Togni and was subsequently formalized by Brešar et al.; its resolution is not specified in the source.