摘要
拓扑学中经典的约当定理指出：一个简单闭曲线Ｃ将球面分割为二个连通区域使得它们的公共边界为Ｃ．本文用与Ｋ５或Ｋ３，３同胚的图给出了图在环面上可嵌入性的一个表征．进而，用不可约图提供了图在一般可定向的曲面上可嵌入性的一个充要条件．同时，对于一般不可定向曲面，特别是射影平面。
The classical version of Jordan curve theorem in topology states that a single closed curve C separates the sphere into two connected components whose common boundary is C. In this paper, graphs homeomorphic to K 3,3 or K 5 are used to describe a characterization of embeddability of graphs on the torus. Furthermore, a necessary and sufficient condition for the embeddability of a graph on general orientable surfaces in terms of the irreducible graphs is provided. For general non-orientable surfaces, a characterization of embeddability especially on the projective plane is provided.
出处
《北方交通大学学报》
CSCD
北大核心
1997年第2期127-136,共10页
Journal of Northern Jiaotong University
关键词
约当曲线
曲面
不可约图
图
可嵌入性
Jordan curve polyhedron K graph surface irreducible graph
