The Uniqueness of Skeleton Presentation of Complete Bipartite Graph $K_{m,n}$
Received:November 02, 2012  Revised:February 19, 2013
Key Word: complete bipartite graph   skeleton presentation   floor   ambient isotopy.  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11271063).
Author NameAffiliation
Lin XIAO School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China 
Guangyan SHEN School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China 
Bin LI School of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. China 
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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.
Citation:
DOI:10.3770/j.issn:2095-2651.2013.05.011
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