# On intrinsically knotted or completely 3-linked graphs

@article{Hanaki2010OnIK,
title={On intrinsically knotted or completely 3-linked graphs},
author={Ryo Hanaki and Ryo Nikkuni and Kouki Taniyama and Akiko Yamazaki},
journal={Pacific Journal of Mathematics},
year={2010},
volume={252},
pages={407-425}
}
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 each of whose 2-component sublinks is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of 4Y-exchanges and Y4-exchanges is a minor-minimal intrinsically knotted or completely 3-linked graph.

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