English

Counting Links and Knots in Complete Graphs

Geometric Topology 2014-12-24 v2 Combinatorics

Abstract

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 K4,4,1K_{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.

Keywords

Cite

@article{arxiv.1008.1085,
  title  = {Counting Links and Knots in Complete Graphs},
  author = {Loren Abrams and Blake Mellor and Lowell Trott},
  journal= {arXiv preprint arXiv:1008.1085},
  year   = {2014}
}

Comments

24 pages, 12 figures; v2 adds an appendix describing the program used to count the links and knots in examples

R2 v1 2026-06-21T15:57:40.579Z