HEPTAGONAL KNOTS AND RADON PARTITIONS

Title & Authors
HEPTAGONAL KNOTS AND RADON PARTITIONS
Huh, Young-Sik;

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 $\small{K_7}$ into $\small{\mathbb{R}^3}$.
Keywords
polygonal knot;gure-eight knot;complete graph;linear embedding;
Language
English
Cited by
1.
KNOTTED HAMILTONIAN CYCLES IN LINEAR EMBEDDING OF K7 INTO ℝ3, Journal of Knot Theory and Its Ramifications, 2012, 21, 14, 1250132
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