Intrinsically Knotted Graphs

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In 1983, Conway and Gordon proved that for every 3D embedding of (the complete graph on seven points), at least one of the 7-cycles would be knotted. The graph is thus called an intrinsically knotted graph.

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Similarly, the graph is intrinsically linked, because it will always contain two linked 3-cycles.

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Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA


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The 23 given point embeddings have the property that no set of four points is on a plane.



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