Linear embeddings of K9 are triple linked
Ramin Naimi, Elena Pavelescu · Journal of Knot Theory and Its Ramifications · 2014
We use the theory of oriented matroids to show that any linear embedding of K9, the complete graph on nine vertices, into 3-space contains a non-split link with three components. This shows that Sachs' conjecture on linear, linkless embeddings of graphs, whether true or false, does not extend to 3-links.