EVERY LINK IS A BOUNDARY OF A COMPLETE BIPARTITE GRAPH K(2,n)
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A voltage assignment on a graph was used to enumer-ate all possible 2-cell embeddings of a graph onto surfaces. The boundary of the surface which is obtained from 0 voltage on every edges of a very special diagram of a complete bipartite graph Km,n is surprisingly the (m, n) torus link. In the present article, we prove that every link is the boundary of a complete bipartite multi-graph Km,n for which voltage assignments are either −1 or 1 and that every link is the boundary of a complete bipartite graph K2,n for which voltage assignments are either −1, 0 or 1 where edges in the diagram of graphs may be linked but not knotted.
Abstract
A voltage assignment on a graph was used to enumer-ate all possible 2-cell embeddings of a graph onto surfaces. The boundary of the surface which is obtained from 0 voltage on every edges of a very special diagram of a complete bipartite graph Km,n is surprisingly the (m, n) torus link. In the present article, we prove that every link is the boundary of a complete bipartite multi-graph Km,n for which voltage assignments are either −1 or 1 and that every link is the boundary of a complete bipartite graph K2,n for which voltage assignments are either −1, 0 or 1 where edges in the diagram of graphs may be linked but not knotted.
참고문헌 (12)
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