Let mad(G) denote the maximum average degree (over all subgraphs) of G and let χi(G) denote the injective chromatic number of G. We prove that if Δ≥4 and , then χi(G)≤Δ+2. When Δ=3, we show that implies χi(G)≤5. In contrast, we give a graph G with Δ=3, , and χi(G)=6.
