THE BOUNDARIES OF DIPOLE GRAPHS AND THE COMPLETE BIPARTITE GRAPHS K2,n

• Journal title : Honam Mathematical Journal
• Volume 36, Issue 2,  2014, pp.399-415
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2014.36.2.399
Title & Authors
THE BOUNDARIES OF DIPOLE GRAPHS AND THE COMPLETE BIPARTITE GRAPHS K2,n
Kim, Dongseok;

Abstract
We study the Seifert surfaces of a link by relating the embeddings of graphs with induced graphs. As applications, we prove that every link L is the boundary of an oriented surface which is obtained from a graph embedding of a complete bipartite graph $\small{K_{2,n}}$, where all voltage assignments on the edges of $\small{K_{2,n}}$ are 0. We also provide an algorithm to construct such a graph diagram of a given link and demonstrate the algorithm by dealing with the links $\small{4^2_1}$ and $\small{5_2}$.
Keywords
Language
English
Cited by
1.
The complete list of prime knots whose flat plumbing basket numbers are 6 or less, Journal of Knot Theory and Its Ramifications, 2015, 24, 07, 1550042
2.
THE BASKET NUMBERS OF KNOTS, Korean Journal of Mathematics, 2015, 23, 1, 115
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