We describe which knots can be obtained as cycles in the canonical book representation of the
complete graph
,
and we conjecture that the canonical book representation of
attains the least possible number of knotted cycles for any embedding of
. The canonical book
representation of
contains a Hamiltonian cycle that is a composite knot if and only if
. When
and
are relatively
prime, the
torus knot is a Hamiltonian cycle in the canonical book representation of
. For each knotted Hamiltonian
cycle
in the canonical
book representation of
,
there are at least
Hamiltonian cycles that are ambient isotopic to
in the canonical book
representation of
.
Finally, we list the number and type of all nontrivial knots
that occur as cycles in the canonical book representation of
for
.
Keywords
spatial graph, intrinsically knotted, canonical book
