平面图加边的直线可画性
Straight-line Drawability of a Planar Graph Plus an Edge
摘要：
本文研究由一个平面图加一条边组成的拓扑图的直线图，也称为准平面图。我们提出了这样的图形，承认一个直线图的特征。该特征使得线性时间测试算法能够确定几乎平面图是否允许直线绘图，以及构造这样的绘图的线性时间绘图算法，如果它存在的话。我们还表明，一些几乎平面图需要指数面积的直线绘图。
英文摘要：
We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing.
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。
