# HEPTAGONAL KNOTS AND RADON PARTITIONS

• Huh, Young-Sik (DEPARTMENT OF MATHEMATICS COLLEGE OF NATURAL SCIENCES HANYANG UNIVERSITY)
• Published : 2011.03.01

#### 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 $\mathbb{R}^3$.

#### Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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#### Cited by

1. KNOTTED HAMILTONIAN CYCLES IN LINEAR EMBEDDING OF K7 INTO ℝ3 vol.21, pp.14, 2012, https://doi.org/10.1142/S0218216512501325