  For a sequence of non-decreasing positive integers $S = (s_1, \ldots, s_k)$,
a packing $S$-coloring is a partition of $V(G)$ into sets $V_1, \ldots, V_k$
such that for each $1\leq i \leq k$ the distance between any two distinct
$x,y\in V_i$ is at least $s_i+1$. The smallest $k$ such that $G$ has a packing
$(1,2, \ldots, k)$-coloring is called the packing chromatic number of $G$ and
is denoted by $\chi_p(G)$. For a graph $G$, let $D(G)$ denote the graph
obtained from $G$ by subdividing every edge. The question whether $\chi_p(D(G))
\le 5$ for all subcubic graphs was first asked by Gastineau and Togni and later
conjectured by Bresar, Klavzar, Rall and Wash. Gastineau and Togni observed
that if one can prove every subcubic graph except the Petersen graph is packing
$(1,1,2,2)$-colorable then the conjecture holds. The maximum average degree,
mad($G$), is defined to be $\max\{\frac{2|E(H)|}{|V(H)|}: H \subset G\}$. In
this paper, we prove that subcubic graphs with $mad(G)<\frac{30}{11}$ are
packing $(1,1,2,2)$-colorable. As a corollary, the conjecture of Bresar et al
holds for every subcubic graph $G$ with $mad(G)<\frac{30}{11}$.

Combinatorics