Knots and links in certain spatial complete graphs
type: Item
instance of: scholarly article
title: Knots and links in certain spatial complete graphs
zbMATH Open document ID: 0858.05038
author: Takashi Otsuki
published in: Journal of Combinatorial Theory. Series B
publication date: 1997-03-23T00:00:00Z
review text: The author proves that in a canonical book representation of \(K_n\) each link consisting of a pair of disjoint 3-cycles is either a trivial link or a Hopf link and the number of such Hopf links is exactly \((\begin{smallmatrix} n\\ 6\end{smallmatrix})\) for \(n\geq6\). Furthermore, each 7-cycle knot is either a trivial knot or a trefoil and the number of such trefoils is exactly \((\begin{smallmatrix} n\\ 7\end{smallmatrix})\) for \(n\geq 7\).
reviewed by: Steven C. Althoen
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C30
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 934822
zbMATH Keywords: complete graph
zbMATH Keywords: Hopf link
zbMATH Keywords: knot
zbMATH Keywords: trefoil
MaRDI profile type: Publication
OpenAlex ID: W2015922922
DOI: 10.1006/JCTB.1996.0054
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description: scientific article; zbMATH DE number 934822