  Let $\mad(G)$ denote the maximum average degree (over all subgraphs) of $G$
and let $\chi_i(G)$ denote the injective chromatic number of $G$. We prove that
if $\Delta\geq 4$ and $\mad(G)<\frac{14}5$, then $\chi_i(G)\leq\Delta+2$. When
$\Delta=3$, we show that $\mad(G)<\frac{36}{13}$ implies $\chi_i(G)\le 5$. In
contrast, we give a graph $G$ with $\Delta=3$, $\mad(G)=\frac{36}{13}$, and
$\chi_i(G)=6$.
