Knots and Links in Certain Spatial Complete Graphs

We give a spatial representation of the complete graphKnwhich contains exactly[formula]Hopf links consisting of pairs of disjoint 3-cycles, where[formula]is the minimum number of pairs of disjoint 3-cycles forming a non-split link contained in any spatial representation ofKn. Furthermore, we show that the above spatial representation ofKncontains exactly[formula]trefoil knots consisting of 7-cycles, where[formula]is the minimum number of 7-cycles forming a non-trivial knot contained in any spatial representation ofKn.