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KNOTTED HAMILTONIAN CYCLES IN LINEAR EMBEDDING OF K₇ INTO ℝ³

YOUNGSIK HUH

Department of Mathematics, College of Natural Sciences, Hanyang University, Seoul 133-791, Korea

https://doi.org/10.1142/S0218216512501325Cited by:4 (Source: Crossref)

Abstract

In 1983 Conway and Gordon proved that any embedding of the complete graph K₇ into ℝ³ contains at least one nontrivial knot as its Hamiltonian cycle. After their work knots (also links) are considered as intrinsic properties of abstract graphs, and numerous subsequent works have been continued until recently. In this paper, we are interested in knotted Hamiltonian cycles in linear embedding of K₇. Concretely it is shown that any linear embedding of K₇ contains at most three figure-8 knots.

Keywords:

AMSC: 57M25, 57M15, 05C10

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