Injective edge chromatic number of sparse graphs

A k-edge coloring phi of graph G is injective if any two edges at distance 2 or in the same triangle get different colors. The minimum k in such an edge coloring is the injective edge chromatic number of G, written as chi i '(G). We prove in this paper that for any graph G with Delta(G)<= 5, chi i '(G)<= 18 if mad(G)<16/5, chi i '(G)<= 19 if mad(G)<(7)/(2) and chi i '(G)<= 20 if mad(G)<(15)/(4).