On packing S-colorings of subcubic graphs

For a sequence S=(s1,s2,…,sk) of positive integers with s1≤s2≤⋯≤sk, a packing S-coloring of a graph G is a partition of V(G) into k subsets V1,V2,…,Vk such that for each 1≤i≤k the distance between any two distinct vertices x,y∈Vi is at least si+1. Gastineau and Togni (2016) posed an open problem: is every 3-irregular subcubic graph packing (1,1,3)-colorable? We show that this is true, improving a known result of Gastineau and Togni: every 3-irregular subcubic graph is packing (1,1,2)-colorable.