The boundaries of dipole graphs and the complete bipartite graphs K_{2,n}

Dongseok Kim

doi:10.5831/hmj.2014.36.2.399

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arXiv · 1302.3829

The boundaries of dipole graphs and the complete bipartite graphs K_{2,n}

Dongseok Kim

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Abstract

We study the Seifert surfaces of a link by relating the embeddings of graphs by using 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 $K_{2,n}$, where all voltage assignments on the edges of $K_{2,n}$ 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 $4_1^2$ and $5_2$.

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Dongseok Kim. 2013-02-15. The boundaries of dipole graphs and the complete bipartite graphs K_{2,n}. https://doi.org/10.5831/hmj.2014.36.2.399

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