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An \emph{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\emph{acyclic chromatic index}, $\chi'_a(G)$, is the smallest number of colorsallowing an acyclic edge-coloring of $G$. Clearly $\chi'_a(G)\ge \Delta(G)$ forevery graph $G$. Cohen, Havet, and M\"{u}ller conjectured that there exists aconstant $M$ such that every planar graph with $\Delta(G)\ge M$ has$\chi'_a(G)=\Delta(G)$. We prove this conjecture.

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