Article
Licensed
Unlicensed
Requires Authentication
Cutting up graphs revisited – a short proof of Stallings' structure theorem
-
Bernhard Krön
Published/Copyright:
November 15, 2010
Abstract
This is a short proof of the existence of finite sets of edges in graphs with more than one end, such that after removing them we obtain two components which are nested with all their isomorphic images. This was first done in “Cutting up graphs” [Dunwoody, Combinatorica 2: 15–23, 1982]. Together with a certain tree construction and some elementary Bass–Serre theory this yields a combinatorial proof of Stallings' theorem on the structure of finitely generated groups with more than one end.
Received: 2010-02-26
Revised: 2010-08-28
Published Online: 2010-11-15
Published in Print: 2010-December
© de Gruyter 2010
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- On asymptotic densities and generic properties in finitely generated groups
- On finite Thurston-type orderings of braid groups
- Subgroup conjugacy problem for Garside subgroups of Garside groups
- The Latin squares and the secret sharing schemes
- A note on the homology of hyperbolic groups
- Cutting up graphs revisited – a short proof of Stallings' structure theorem
- Some geodesic problems in groups
- Search and witness problems in group theory
- Algebraic attacks using SAT-solvers
Articles in the same Issue
- On asymptotic densities and generic properties in finitely generated groups
- On finite Thurston-type orderings of braid groups
- Subgroup conjugacy problem for Garside subgroups of Garside groups
- The Latin squares and the secret sharing schemes
- A note on the homology of hyperbolic groups
- Cutting up graphs revisited – a short proof of Stallings' structure theorem
- Some geodesic problems in groups
- Search and witness problems in group theory
- Algebraic attacks using SAT-solvers
