所有顶点均位于外面上的外部障碍表示
Outside-Obstacle Representations with All Vertices on the Outer Face
AI总结：
本文研究单障碍位于外面的外部障碍表示，证明每个偏2-树均存在OOR，并刻画或构造若干图类的凸OOR与正OOR。
摘要：
图 $G$ 的障碍表示由一组多边形障碍以及将 $G$ 绘制成相对于这些障碍的可见性图组成：顶点被映射为点，边被映射为直线段，使得每条边都避开所有障碍，而每条非边都与至少一个障碍相交。过去几年中，障碍表示得到了相当深入的研究。本文聚焦于外部障碍表示（OOR），这种表示仅在绘图的外面中使用一个障碍。已知每个外平面图都允许这种表示。我们加强了这一结果，证明每个（偏）2-树都具有 OOR。我们还考虑了 OOR 的受限版本，其中图的顶点形成凸多边形，甚至形成正多边形。我们刻画了树的补图以及完全图去掉一个简单环何时允许凸 OOR。我们为所有（偏）外路、仙人掌图和网格构造了正 OOR。
英文摘要：
An obstacle representation of a graph $G$ consists of a set of polygonal obstacles and a drawing of $G$ as a visibility graph with respect to the obstacles: vertices are mapped to points and edges to straight-line segments such that each edge avoids all obstacles whereas each non-edge intersects at least one obstacle. Obstacle representations have been investigated quite intensely over the last few years. Here we focus on outside-obstacle representations (OORs) that use only one obstacle in the outer face of the drawing. It is known that every outerplanar graph admits such a representation. We strengthen this result by showing that every (partial) 2-tree has an OOR. We also consider restricted versions of OORs where the vertices of the graph form a convex polygon or even a regular polygon. We characterize when the complement of a tree and when a complete graph minus a simple cycle admits a convex OOR. We construct regular OORs for all (partial) outerpaths, cactus graphs, and grids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
