完全二部图$K_{m,n}$的框架表示的唯一性

The Uniqueness of Skeleton Presentation of Complete Bipartite Graph $K_{m,n}$

中文关键词:  完全二部图  框架表示  层  固边合痕

英文关键词:complete bipartite graph  skeleton presentation  floor  ambient isotopy.

中文摘要:

      Kobayashi讨论了空间图在三维流形中的一类标准嵌入,给出了书册表示的概念,并证明了空间图$K_n$的书册表示的最少页是页变换与固边合痕意义下的不变量.本文给出了完全二部图$K_{m,n}$的框架表示的概念,并且证明了完全二部图的框架表示的最小层是层变换与固边合痕意义下的不变量.

英文摘要:

      Kobayashi discussed some kinds of standard embeddings into 3-manifolds of spatial graphs. He introduced the concept of book presentation, which is a standard embedding of spatial graphs with good properties, and proved that the book presentation of minimum sheets of $K_n$ is unique up to the sheet translation and the ambient isotopy. In this present paper we give the definition of skeleton presentation of spatial graphs, and prove that the skeleton presentation of minimum floors of a complete bipartite graph $K_{m,n}$ is unique up to ambient isotopy.