We show that for every m in N, there exists an n in N
such that every embedding of the complete graph Kn
in R3 contains a link of two components whose linking
number is at least m. Furthermore, there exists an r in N
such that every embedding of Kr in R3 contains
a knot Q with |a2(Q)| ≥ m, where a2(Q)
denotes the second coefficient of the Conway polynomial of Q.