Acyclic edge coloring of sparse graphs

Let Δ denote the maximum degree of a graph. Fiamčík first, Alon, Sudakov and Zaks later conjectured that every graph is acyclically edge ( Δ + 2 ) -colorable. In this paper, we prove this conjecture for graphs with maximum average degree less than 4. As a corollary, triangle-free planar graphs are acyclically edge ( Δ + 2 ) -colorable.