  For non-decreasing sequence of integers $S=(a_1,a_2, \dots, a_k)$, an
$S$-packing coloring of $G$ is a partition of $V(G)$ into $k$ subsets
$V_1,V_2,\dots,V_k$ such that the distance between any two distinct vertices
$x,y \in V_i$ is at least $a_{i}+1$, $1\leq i\leq k$. We consider the
$S$-packing coloring problem on subclasses of subcubic graphs: For $0\le i\le
3$, a subcubic graph $G$ is said to be $i$-saturated if every vertex of degree
3 is adjacent to at most $i$ vertices of degree 3. Furthermore, a vertex of
degree 3 in a subcubic graph is called heavy if all its three neighbors are of
degree 3, and $G$ is said to be $(3,i)$-saturated if every heavy vertex is
adjacent to at most $i$ heavy vertices. We prove that every 1-saturated
subcubic graph is $(1,1,3,3)$-packing colorable and $(1,2,2,2,2)$-packing
colorable. We also prove that every $(3,0)$-saturated subcubic graph is
$(1,2,2,2,2,2)$-packing colorable.
