Give a graph G, we color its all edges. If any two adjacent edges gets the different colors, then we call this color a proper edge coloring of G. Give a proper edge coloring of G, if only two colors alternately appear on a cycle, then the cycle is called bichromatic. Acyclic edge coloring of a graph G means that there are no bichromatic cycles in G. The acyclic chromatic index of a graph G is the minimum number k such that G has an acyclic edge coloring using k colors. Denoted \({\chi ^{'}_a}(G)\) as the acyclic chromatic index of G. A planar graph is a graph that can be embedded in the plane in such a way that no two edges intersect geometrically except at a vertex to which they are both incident. In this paper, we use the discharging method to prove that \({\chi ^{'}_a}(G)\le \varDelta (G)+ 2\) if G is a planar graph and there is an integer \(k_v \in \{3, 4, 5\}\) such that v is not contained in any \(k_v\)-cycle for every vertex v.

给图G，我们给它的所有边缘着色。如果任意两个相邻的边缘获得不同的颜色，则我们将此颜色称为G的适当边缘着色。给定适当的G边缘着色，如果一个周期上仅交替出现两种颜色，则该周期称为双色。无环边缘的曲线图的着色ģ手段，有在不双色周期ģ。图G的非循环色指数是最小数k，使得G具有使用k种颜色的非循环边缘着色。表示\（{\志^ {'} _一个}（G）\）作为无环色指数ģ。平面图是可以以这样的方式嵌入平面中的图：除了两个边都入射到的顶点以外，没有两个边在几何上相交。在本文中，我们使用放电方法来证明\（{\志^ {'} _一个}（G）\文件\ varDelta（G）+ 2 \）如果G ^是一个平面图形和存在一个整数\（ k_v \在\ {3，4，5 \} \） ，使得v不包含在任何\（k_v \） -cycle每顶点v。