Knots and links in certain spatial complete graphs (Q1924155)

The author proves that in a canonical book representation of \(K_n\) each link consisting of a pair of disjoint 3-cycles is either a trivial link or a Hopf link and the number of such Hopf links is exactly \((\begin{smallmatrix} n\\ 6\end{smallmatrix})\) for \(n\geq6\). Furthermore, each 7-cycle knot is either a trivial knot or a trefoil and the number of such trefoils is exactly \((\begin{smallmatrix} n\\ 7\end{smallmatrix})\) for \(n\geq 7\).