论文标题
关于向上平面的拓扑性质的评论
Remark on topological nature of upward planarity
论文作者
论文摘要
图理论中向上平面图的概念以及类别理论中的渐进平面图（或平面字符串图）的概念本质上是同一件事。在本文中，我们将思想和类别理论中的思想结合在一起，以解释原因以及在什么意义上向上平面性是一种拓扑特性。主要的结果是，当且仅当它们通过平面同位素连接时，它们是等效的（通过变形连接）的两个向上平面图等效（通过变形连接），该平面同位素是保留$ g $的方向和极化的平面同位素。该结果对塞林格的猜想提供了积极的答案，后者的策略与Delpeuch和Vicary最近给出的解决方案不同。
The notion of an upward plane graph in graph theory and that of a progressive plane graph (or plane string diagram) in category theory are essentially the same thing. In this paper, we combine the ideas in graph theory and category theory to explain why and in what sense upward planarity is a topological property. The main result is that two upward planar drawings of an acyclic directed graph are equivalent (connected by a deformation) if and only if they are connected by a planar isotopy which preserves the orientation and polarization of $G$. This result gives a positive answer to Selinger's conjectue, whose strategy is different from the solution recently given by Delpeuch and Vicary.
