The subdivision packing-coloring conjecture for subcubic graphs

Let $G$ be a subcubic graph, meaning that every vertex of $G$ has degree at most $3$, and let $S(G)$ be the graph obtained by subdividing every edge of $G$ exactly once. A $(1,2,3,4,5)$-packing coloring assigns one of five colors to the vertices so that vertices receiving color $i$ are pairwise at distance greater than $i$.

Subdivision packing-coloring conjecture. The graph $S(G)$ admits a $(1,2,3,4,5)$-packing coloring. Equivalently, every subdivision of a subcubic graph has packing chromatic number at most $5$.

This conjecture was posed by Brešar, Klavžar, Rall, and Wash following a question of Gastineau and Togni. The supplied source evidence establishes it for generalized prisms of a cycle, except for the Petersen graph; the general statement is therefore recorded as solved according to the supplied status.