2025/01/09 by Huang, Danjun, Guo, Yuqian
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.04953
An injective k-edge-coloring of a graph G is a mapping ϕ: E(G)→\1,2,...,k\, such that ϕ(e)≠ϕ(e') if edges e and e' are at distance two, or are in a triangle. The smallest integer k such that G has an injective k-edge-coloring is called the injective chromatic index of G, denoted by χi'(G). In this paper, we prove that χi'(G)≤ 7 for every graph G with Δ(G)≤ 4 and mad(G)<(8)/(3), where Δ(G) is the maximum degree of G.