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Links inside StraightEdge Embeddings of Complete Bipartite Graphs

We prove the following theorem. Let L be any link. There is some N = NL such that every straight-edge embedding of the complete bipartite graph KN,N contains a finite union of cycles having link type L. This result builds on the ideas of S. Negami, who proved the analogous result for complete graphs. Most of our motivation for this paper is to give a simpler proof of Negami’s Theorem.