An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic edge coloring conjecture by Fiamčik (1978) and Alon, Sudakov and Zaks (2001) states that every simple graph with maximum degree Δ is acyclically edge $(\mathrm{\Delta }+2)$-colorable. Despite many milestones, the conjecture remains open even for planar graphs. In this paper, we confirm affirmatively the conjecture on planar graphs without intersecting triangles. We do so by first showing, by discharging methods, that every planar graph without intersecting triangles must have at least one of the six specified groups of local structures, and then proving the conjecture by recoloring certain edges in each such local structure and by induction on the number of edges in the graph.

图G的非循环边着色是适当的边着色，从而不会产生双色循环。Fiamčik (1978) 和 Alon、Sudakov 和 Zaks (2001) 的非循环边着色猜想指出，每个具有最大度数 Δ 的简单图都是非循环边$(\mathrm{\Delta }+2)$-可着色。尽管有许多里程碑，但即使对于平面图，这个猜想仍然是开放的。在本文中，我们肯定地证实了关于没有相交三角形的平面图的猜想。我们首先通过放电方法证明每个没有相交三角形的平面图必须至少具有六个指定的局部结构组中的一个，然后通过重新着色每个这样的局部结构中的某些边并通过归纳图中的边数。