A Stallings' type theorem for quasi-transitive graphs
Combinatorics
2019-06-19 v2
Abstract
We consider infinite connected quasi-transitive locally finite graphs and show that every such graph with more than one end is a tree amalgamation of two other such graphs. This can be seen as a graph-theoretical version of Stallings' splitting theorem for multi-ended finitely generated groups and indeed it implies this theorem. It will also lead to a characterisation of accessible graphs in terms of tree amalgamations. We obtain applications of our results for hyperbolic graphs, planar graphs and graphs without any thick end. The application for planar graphs answers a question of Mohar in the affirmative.
Cite
@article{arxiv.1812.06312,
title = {A Stallings' type theorem for quasi-transitive graphs},
author = {Matthias Hamann and Florian Lehner and Babak Miraftab and Tim Rühmann},
journal= {arXiv preprint arXiv:1812.06312},
year = {2019}
}
Comments
24 pages