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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus


CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2018: 0.38

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1869-6104
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Cutting up graphs revisited – a short proof of Stallings' structure theorem

Bernhard Krön
Published Online: 2010-11-15 | DOI: https://doi.org/10.1515/gcc.2010.013

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.

Keywords.: Stallings Theorem on groups with more than one end; structure trees

About the article

Received: 2010-02-26

Revised: 2010-08-28

Published Online: 2010-11-15

Published in Print: 2010-12-01


Citation Information: Groups – Complexity – Cryptology, Volume 2, Issue 2, Pages 213–221, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc.2010.013.

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[2]
VOLKER DIEKERT and ARMIN WEIß
International Journal of Algebra and Computation, 2013, Volume 23, Number 03, Page 611
[3]
M. J. Dunwoody and B. Krön
Journal of Graph Theory, 2015, Volume 80, Number 2, Page 136

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