ACYCLIC EDGE-COLORING OF PLANAR GRAPHS: Δ COLORS SUFFICE WHEN Δ IS LARGE

An acyclic edge-coloring of a graph G is a proper edge-coloring of G such that the subgraph induced by any two color classes is acyclic. The acyclic chromatic index, chi'(a)(G), is the smallest number of colors allowing an acyclic edge-coloring of G. Clearly chi'(a)(G) >= Delta(G) for every graph G. Cohen, Havet, and Muller conjectured that there exists a constant M such that every planar graph with Delta(G) >= M has chi'(a)(G) - Delta(G). We prove this conjecture.