Anto, N.Basavaraju, M.Hegde, S.M.Kulamarva, S.2026-02-042024Discrete Mathematics, 2024, 347, 4, pp. -0012365Xhttps://doi.org/10.1016/j.disc.2024.113898https://idr.nitk.ac.in/handle/123456789/21209An acyclic edge coloring of a graph is a proper edge coloring without any bichromatic cycles. The acyclic chromatic index of a graph G denoted by a′(G), is the minimum k such that G has an acyclic edge coloring with k colors. Fiamčík [10] conjectured that a′(G)≤Δ+2 for any graph G with maximum degree Δ. A graph G is said to be k-degenerate if every subgraph of G has a vertex of degree at most k. Basavaraju and Chandran [4] proved that the conjecture is true for 2-degenerate graphs. We prove that for a 3-degenerate graph G, a′(G)≤Δ+5, thereby bringing the upper bound closer to the conjectured bound. We also consider k-degenerate graphs with k≥4 and give an upper bound for the acyclic chromatic index of the same. © 2024 Elsevier B.V.3-degenerate graphsAcyclic chromatic indexAcyclic edge coloringk-degenerate graphs