Let $k$ be a non-negative integer. Then any embedding of the complete graph on $6\cdot2^k$ vertices into a three-space contains a two-component link whose absolute value of the linking number is greater than or equal to $2^k$. Let $j$ be a non-negative integer. Then any embedding of the complete graph on $48\cdot2^j$ vertices into a three-space contains a knot whose absolute value of the second coefficient of the Conway polynomial is greater than or equal to $2^{2j}$.