Minimally knotted embeddings of planar graphs
type: Item
instance of: scholarly article
title: Minimally knotted embeddings of planar graphs
zbMATH Open document ID: 0789.57006
DOI: 10.1007/BF02572430
author: Ying-Qing Wu
published in: Mathematische Zeitschrift
publication date: 1994-05-30T00:00:00Z
full work available at URL: https://eudml.org/doc/174592
review text: A graph \(\Gamma\) in \(S^ 3\) is called minimally knotted if \(\Gamma\) is knotted, but all of its proper subgraphs are unknotted. It was conjectured that any abstractly planar graph with no free edges admits a minimally knotted embedding into the 3-sphere. \textit{L. Kawauchi} [Hyperbolic imitation of 3-manifolds (Preprint 1987)] gave a proof of this conjecture, using his ``hyperbolic imitations'' method. The purpose of this paper is to give a simpler and elementary proof of this result.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 567432
zbMATH Keywords: graph in \(S^ 3\)
zbMATH Keywords: minimally knotted
MaRDI profile type: Publication
cites work: Q3806376
cites work: Minimally knotted graphs in \(S^ 3\)
description: scientific article; zbMATH DE number 567432