Acyclic edge-coloring of planar graphs: $\\Delta$ colors suffice when\n $\\Delta$ is large

An \\emph{acyclic edge-coloring} of a graph $G$ is a proper edge-coloring of\n$G$ such that the subgraph induced by any two color classes is acyclic. The\n\\emph{acyclic chromatic index}, $\\chi'_a(G)$, is the smallest number of colors\nallowing an acyclic edge-coloring of $G$. Clearly $\\chi'_a(G)\\ge \\Delta(G)$ for\nevery graph $G$. Cohen, Havet, and M\\"{u}ller conjectured that there exists a\nconstant $M$ such that every planar graph with $\\Delta(G)\\ge M$ has\n$\\chi'_a(G)=\\Delta(G)$. We prove this conjecture.\n