Counting Links and Knots in Complete Graphs

Loren Abrams; Blake Mellor; Lowell Trott

Counting Links and Knots in Complete Graphs

Loren Abrams, Blake Mellor, Lowell Trott

Loyola Marymount University

Research output: Other contribution

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 language	Undefined/Unknown
State	Published - Jan 1 2013

Publication series

Name	Mathematics, Statistics and Data Science Faculty Works

Access to Document

http://digitalcommons.lmu.edu/math_fac/102

Cite this

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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 K4,4,1 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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AB - 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 K4,4,1 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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T3 - Mathematics, Statistics and Data Science Faculty Works

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