论文标题
无环的着色猜想在平面图上是正确的，而无需与三角形相交
Acyclic edge coloring conjecture is true on planar graphs without intersecting triangles
论文作者
论文摘要
图$ g $的无环着着色是适当的边缘着色，因此不会产生双重周期。 Fiam {č} IK（1978）和Alon，Sudakov and Zaks（2001）的无环着色猜想指出，每个具有最大程度$δ$的简单图都是非常周期性的边缘$（δ+ 2）$ - 可着色。尽管有许多里程碑，但对于平面图，猜想仍然开放。在本文中，我们肯定地确认了平面图上的猜想，而无需与三角形相交。我们首先通过放电方法来表明，每个没有相交三角形的平面图必须至少具有指定的局部结构组中的至少一个，然后通过在每个这样的局部结构中重新上色和诱导图中的边数来证明猜想。
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 Fiam{č}ik (1978) and Alon, Sudakov and Zaks (2001) states that every simple graph with maximum degree $Δ$ is acyclically edge $(Δ+ 2)$-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.
