Minimally knotted embeddings of planar graphs (Q1323433)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Minimally knotted embeddings of planar graphs |
scientific article; zbMATH DE number 567432
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimally knotted embeddings of planar graphs |
scientific article; zbMATH DE number 567432 |
Statements
Minimally knotted embeddings of planar graphs (English)
0 references
30 May 1994
0 references
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.
0 references
graph in \(S^ 3\)
0 references
minimally knotted
0 references
