We examine K n , the canonical book representation of the complete graph K n , and describe knots that can be obtained as cycles in this particular spatial embedding. We prove that for each knotted Hamiltonian cycle α in K n , there are at least 2 k n+k k Hamiltonian cycles that are ambient isotopic to α in K n+k . We show that when p and q are relatively prime with p < q, the (p, q) torus knot is a Hamiltonian cycle in K 2p+q .We also show that the canonical book representation of K n contains a Hamiltonian cycle that is a composite knot if and only if n ≥ 12. We prove that if α is a knotted cycle in the canonical book representation of K n and β is a knotted cycle in the canonical book representation of K m , then there is a Hamiltonian cycle in K n+m+1 that is ambient isotopic to a composite knot α#β. 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 ≤ 11.
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