摘要
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 .