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On intrinsically knotted or completely 3-linked graphs

Ryo Hanaki, Ryo Nikkuni, Kouki Taniyama, Akiko Yamazaki
Arxiv ID: 1006.0698Last updated: 5/19/2020
We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link any of whose 2-component sublink is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of $\triangle Y$-exchanges and $Y \triangle$-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.

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