Liu–Zhang–Zhang conjecture on packing colorings of subcubic graphs

A packing $(1,1,2,2)$-coloring of a graph is a partition of its vertex set into four classes whose pairwise vertex distances are respectively at least $2$, $2$, $3$, and $3$. Liu–Zhang–Zhang conjecture. Every connected subcubic graph except the Petersen graph is packing $(1,1,2,2)$-colorable. The supplied text presents this as a stronger conjecture related to the subdivision conjecture, and the current status is not specified there.