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Knots and Links in Certain Spatial Complete Graphs

✍ Scribed by Takashi Otsuki

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
311 KB
Volume
68
Category
Article
ISSN
0095-8956

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✦ Synopsis

We give a spatial representation of the complete graph K n which contains exactly ( n 6 ) Hopf links consisting of pairs of disjoint 3-cycles, where ( n 6 ) is the minimum number of pairs of disjoint 3-cycles forming a non-split link contained in any spatial representation of K n . Furthermore, we show that the above spatial representation of K n contains exactly ( n 7 ) trefoil knots consisting of 7-cycles, where ( n 7 ) is the minimum number of 7-cycles forming a non-trivial knot contained in any spatial representation of K n .

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