  We describe which knots can be obtained as cycles in the canonical book
representation of K_n, the complete graph on n vertices. We show that the
canonical book representation of K_n contains a Hamiltonian cycle that is a
composite knot if and only if n>11 and we show that when p and q are relatively
prime, the (p,q) torus knot is a Hamiltonian cycle in the canonical book
representation of K_{2p+q}. Finally, we list the number and type of all
non-trivial knots that occur as cycles in the canonical book representation of
K_n for n<12. We conjecture that the canonical book representation of K_n
attains the least possible number of knotted cycles for any embedding of K_n.
