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 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