Knots in certain spatial graphs
type: Item
instance of: scholarly article
title: Knots in certain spatial graphs
zbMATH Open document ID: 0669.57001
author: Miki Shimabara
published in: Tokyo Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: \textit{J. H. Conway} and \textit{C. McA. Gordon} [Knots and liks in spatial graphs, J. Graph Theory 7, 445-453 (1983; Zbl 0524.05028)] showed that every embedding of the complete graph \(K_ 7\) in the three-dimensional Euclidean space \(R^ 3\) contains a knotted cycle. In the present paper their method is generalized. A special case of the result obtained is that every embedding of the complete bipartite graph \(K_{5,5}\) in \(R^ 3\) contains a knotted cycle.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M15
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 4096382
zbMATH Keywords: embedding
zbMATH Keywords: complete bipartite graph
zbMATH Keywords: knotted cycle
reviewed by: Arthur T. White
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270133985
OpenAlex ID: W2028112400
DOI: 10.3836/TJM/1270133985
description: scientific article; zbMATH DE number 4096382