A sufficient condition for intrinsic knotting of bipartite graphs

Sophy Huck; Alexandra Appel; Miguel-Angel Manrique; Thomas W Mattman

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arXiv · 0811.0036

A sufficient condition for intrinsic knotting of bipartite graphs

Sophy Huck·Alexandra Appel·Miguel-Angel Manrique·Thomas W Mattman

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Abstract

We present evidence in support of a conjecture that a bipartite graph with at least five vertices in each part and |E(G)| \geq 4 |V(G)| - 17 is intrinsically knotted. We prove the conjecture for graphs that have exactly five or exactly six vertices in one part. We also show that there is a constant C_n such that a bipartite graph with exactly n \geq 5 vertices in one part and |E(G)| \geq 4 |V(G)| + C_n is intrinsically knotted. Finally, we classify bipartite graphs with ten or fewer vertices with respect to intrinsic knotting.

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Sophy Huck, Alexandra Appel, Miguel-Angel Manrique, Thomas W Mattman. 2008-10-31. A sufficient condition for intrinsic knotting of bipartite graphs. https://arxiv.org/abs/0811.0036

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