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

Details Cutting up graphs revisited - a short proof of Stallings' structure theorem Cutting up graphs revisited - a short proof of Stallings' structure theorem

2010-03-04

arxiv.org/abs/1003.1096v1

Mathematics

Group Theory

12 pages

Scientific paper

This is a new and short proof of the main theorem of classical structure tree theory. Namely, we show the existence of certain automorphism-invariant tree-decompositions of graphs based on the principle of removing finitely many edges. This was first done in "Cutting up graphs" by M.J. Dunwoody. The main ideas are based on the paper "Vertex cuts" by M.J. Dunwoody and the author. We extend the theorem to a detailed combinatorial proof of J.R. Stallings' theorem on the structure of finitely generated groups with more than one end.

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