2025/09/11 by Huang, Danjun, Guo, Yuqian
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2509.09407
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). A graph is called claw-free if it has no induced subgraph isomorphic to the complete bipartite graph K1,3. In this paper, we show that χi'(G)≤ 13 for every claw-free graph G with Δ(G)≤ 4, where Δ(G) is the maximum degree of G.