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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Danjun Huang
Zhejiang Normal University
Electrical & Electronics Engineering

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Injective edge-coloring of claw-free graphs with maximum degree 4 Danjun Huang; Yuqian Guo
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (2026): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2026.14.2.6

Abstract

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 χ′i(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 χ′i(G) ≤ 13 for every claw-free graph G with Δ(G) ≤ 4, where Δ(G) is the maximum degree of G.
Co-Authors Yuqian Guo