| 完全二部图$K_{m,n}$的框架表示的唯一性 |
| |
| 引用本文： | 肖林,沈广艳,李宾. 完全二部图$K_{m,n}$的框架表示的唯一性[J]. 数学研究及应用, 2013, 33(5): 616-624 |
| |
| 作者姓名： | 肖林 沈广艳 李宾 |
| |
| 作者单位： | 东北师范大学数学与统计学院, 吉林 长春 130024;东北师范大学数学与统计学院, 吉林 长春 130024;东北师范大学数学与统计学院, 吉林 长春 130024 |
| |
| 基金项目： | 国家自然科学基金(Grant No.11271063). |
| |
| 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.
|
| 关 键 词： | 完全二部图；框架表示；层；固边合痕 |
| 收稿时间： | 2012-11-02 |
| 修稿时间： | 2013-02-19 |
The Uniqueness of Skeleton Presentation of Complete Bipartite Graph $K_{m,n}$ |
| |
| Lin XIAO,Guangyan SHEN and Bin LI. The Uniqueness of Skeleton Presentation of Complete Bipartite Graph $K_{m,n}$[J]. Journal of Mathematical Research with Applications, 2013, 33(5): 616-624 |
| |
| Authors: | Lin XIAO Guangyan SHEN Bin LI |
| |
| Affiliation: | School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China;School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China;School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China |
| |
| Abstract: | 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. |
| |
| Keywords: | complete bipartite graph skeleton presentation floor ambient isotopy. |
|
| 点击此处可从《数学研究及应用》浏览原始摘要信息 |
|
点击此处可从《数学研究及应用》下载全文 |
|
