论文标题
在平面上有星形边界的图形图上的注释
A note on graph drawings with star-shaped boundaries in the plane
论文作者
论文摘要
在本说明中，我们提出了一种直接的方法，可以产生平面图的直线嵌入，其中图的一个面固定在平面上作为星形多边形。它基于最小化离散的dirichlet能量，遵循图特嵌入定理的想法。我们将其称为星形多边形的大地测量。此外，我们研究了所有直线嵌入的空间的同质属性。我们提出一个简单的论点，以表明如果边界是一个非凸口四边形，则该空间是可缩合的。我们猜测，同一陈述对于一般的星形多边形。
In this note, we propose a straightforward method to produce an straight-line embedding of a planar graph where one face of a graph is fixed in the plane as a star-shaped polygon. It is based on minimizing discrete Dirichlet energies, following the idea of Tutte's embedding theorem. We will call it a geodesic triangulation of the star-shaped polygon. Moreover, we study the homotopy property of spaces of all straight-line embeddings. We give a simple argument to show that this space is contractible if the boundary is a non-convex quadrilateral. We conjecture that the same statement holds for general star-shaped polygons.
