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December 2013 Counting Links and Knots in Complete Graphs
Loren ABRAMS, Blake MELLOR, Lowell TROTT
Tokyo J. Math. 36(2): 429-458 (December 2013). DOI: 10.3836/tjm/1391177980

Abstract

We investigate the minimal number of links and knots in embeddings of complete partite graphs in $S^3$. 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.

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Loren ABRAMS. Blake MELLOR. Lowell TROTT. "Counting Links and Knots in Complete Graphs." Tokyo J. Math. 36 (2) 429 - 458, December 2013. https://doi.org/10.3836/tjm/1391177980

Information

Published: December 2013
First available in Project Euclid: 31 January 2014

zbMATH: 1285.05036
MathSciNet: MR3161567
Digital Object Identifier: 10.3836/tjm/1391177980

Subjects:
Primary: 05C10
Secondary: 57M25

Rights: Copyright © 2013 Publication Committee for the Tokyo Journal of Mathematics

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Vol.36 • No. 2 • December 2013
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