Acyclic chromatic indices of planar graphs with large girth

An acyclic edge coloring of a graph GG is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index a′(G)a′(G) of GG is the smallest kk such that GG has an acyclic edge coloring using kk colors.In this paper, we prove that every planar graph GG with girth g(G)g(G) and maximum degree ΔΔ has a′(G)=Δa′(G)=Δ if there exists a pair (k,m)∈{(3,11),(4,8),(5,7),(8,6)}(k,m)∈{(3,11),(4,8),(5,7),(8,6)} such that GG satisfies Δ≥kΔ≥k and g(G)≥mg(G)≥m.