Counting Links and Knots in Complete Graphs

Authors

Loren Abrams
Blake Mellor, Loyola Marymount UniversityFollow
Lowell Trott

Document Type

Article - pre-print

Publication Date

2013

Abstract

We investigate the minimal number of links and knots in embeddings of complete partite graphs in S³. 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 in an embedding of 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.

Original Publication Citation

Abrams, Loren; Mellor, Blake; Trott, Lowell. Counting Links and Knots in Complete Graphs. Tokyo J. of Math. 36 (2013), no. 2, 429--458. doi:10.3836/tjm/1391177980.

Publisher Statement

This is an author-manuscript of an article accepted for publication in Tokyo Journal of Mathematics following peer review. The version of record is available online at: doi:10.3836/tjm/1391177980.

Digital Commons @ LMU & LLS Citation

Abrams, Loren; Mellor, Blake; and Trott, Lowell, "Counting Links and Knots in Complete Graphs" (2013). Mathematics, Statistics and Data Science Faculty Works. 102.
https://digitalcommons.lmu.edu/math_fac/102