Intersection number and stability of some inscribable graphs
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- 作者：Jinsong Liu ; Ze Zhou
- 关键词：Inscribable graph ; Stability ; Intersection number ; Circle pattern
- 刊名：Geometriae Dedicata
- 出版年：2016
- 出版时间：December 2016
- 年：2016
- 卷：185
- 期：1
- 页码：105-121
- 全文大小：743 KB
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Geometry - 出版者：Springer Netherlands
- ISSN：1572-9168
- 卷排序：185
文摘
A planar graph is inscribable if it is combinatorial equivalent to the skeleton of an inscribed polyhedron in the unit sphere \(\mathbb {S}^2\). Giving an inscribable graph, in its combinatorial equivalent class if we could also find a polyhedron inscribed in each convex surface sufficiently close to the unit sphere \(\mathbb {S}^2\), then we call such an inscribable graph a stable one. By combining the Teichmüller theory of packings with differential topology method, in this paper we shall investigate the stability of some inscribable graphs.