SS-packing colorings of cubic graphs

Given a non-decreasing sequence S=(s1,s2,…,sk)S=(s1,s2,…,sk) of positive integers, an SS-packing coloring   of a graph GG is a mapping cc from V(G)V(G) to {s1,s2,…,sk}{s1,s2,…,sk} such that any two vertices with the iith color are at mutual distance greater than sisi, 1≤i≤k1≤i≤k. This paper studies SS-packing colorings of (sub)cubic graphs. We prove that subcubic graphs are (1,2,2,2,2,2,2)(1,2,2,2,2,2,2)-packing colorable and (1,1,2,2,2)(1,1,2,2,2)-packing colorable. For subdivisions of subcubic graphs we derive sharper bounds, and we provide an example of a cubic graph of order 38 which is not (1,2,…,12)(1,2,…,12)-packing colorable.