Acyclic edge coloring of planar graphs without 4-cycles

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index a'(G) of G is the smallest integer k such that G has an acyclic edge coloring using k colors. Fiamik (Math. Slovaca 28:139-145, 1978) and later Alon, Sudakov and Zaks (J. Graph Theory 37:157-167, 2001) conjectured that a'(G)a parts per thousand currency sign Delta+2 for any simple graph G with maximum degree Delta. In this paper, we confirm this conjecture for planar graphs G with Delta not equal 4 and without 4-cycles.