Improved bounds on acyclic edge colouring

We prove that the acyclic chromatic index a′(G)⩽6Δa′(G)⩽6Δ for all graphs with girth at least 99. We extend the same method to obtain a bound of 4.52Δ4.52Δ with the girth requirement g⩾220g⩾220. We also obtain a relationship between gg and a′(G)a′(G).