Loren Abrams, Blake Mellor, Lowell Trott
Published 2010-08-05, updated 2013-06-21Version 2
We investigate the minimal number of links and knots in complete partite graphs. We provide exact values or bounds on the minimal number of links for all complete partite graphs with all but 4 vertices in one partition, or with 9 vertices in total. In particular, we find that the minimal number of links for $K_{4,4,1}$ is 74. We also provide exact values or bounds on the minimal number of knots for all complete partite graphs with 8 vertices.
Comments: 24 pages, 12 figures; v2 adds an appendix describing the program used to count the links and knots in examples
Intrinsic knotting and linking of almost complete partite graphs
Intrinsic knotting and linking of almost complete graphs
On Virtual Crossing Numbers for Virtual Knots
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