On r-acyclic edge colorings of planar graphs

A proper edge coloring of is -acyclic if every cycle contained in is colored with at least colors. The -acyclic chromatic index of a graph, denoted by , is the minimum number of colors required to produce an -acyclic edge coloring. In this paper, we study 4-acyclic edge colorings by proving that for every planar graph, for every series–parallel graph and for every outerplanar graph. In addition, we prove that every planar graph with maximum degree at least and girth at least has for every .