Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2011; 48(2): 367-382

Printed March 1, 2011

https://doi.org/10.4134/JKMS.2011.48.2.367

Copyright © The Korean Mathematical Society.

Heptagonal knots and Radon partitions

Youngsik Huh

Hanyang University

Abstract

We establish a necessary and sufficient condition for a heptagonal knot to be figure-8 knot. The condition is described by a set of Radon partitions formed by vertices of the heptagon. In addition we relate this result to the number of nontrivial heptagonal knots in linear embeddings of the complete graph $K_7$ into $\mathbb{R}^3$.

Keywords: polygonal knot, figure-eight knot, complete graph, linear embedding

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