Tokyo Journal of Mathematics

Counting Links and Knots in Complete Graphs

Loren ABRAMS, Blake MELLOR, and Lowell TROTT

Full-text: Open access

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.

Article information

Source
Tokyo J. Math., Volume 36, Number 2 (2013), 429-458.

Dates
First available in Project Euclid: 31 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1391177980

Digital Object Identifier
doi:10.3836/tjm/1391177980

Mathematical Reviews number (MathSciNet)
MR3161567

Zentralblatt MATH identifier
1285.05036

Subjects
Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Citation

ABRAMS, Loren; MELLOR, Blake; TROTT, Lowell. Counting Links and Knots in Complete Graphs. Tokyo J. Math. 36 (2013), no. 2, 429--458. doi:10.3836/tjm/1391177980. https://projecteuclid.org/euclid.tjm/1391177980


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References

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