Triviality of function $\omega_2$ for spatial complete graphs

Let $G_n$, $n\geqslant 6$, be a complete spatial graph with $n$ vertices. In 1983 J. Y. Conway and C. McA. Gordon introduced function $\omega_2$ for all such graphs with 6 vertices. They proved that $\omega_2(G_6) = 1$ for any spatial graph $G_6$, and hence any such graph contains non-trivial link. In present work we prove that $\omega_2(G_n) = 0$ for any spatial complete graph $G_n$ with $n\geqslant 7$ vertices.