Asymptotic dimension of multi-ended quasi-transitive graphs
Combinatorics
2019-12-06 v1
Abstract
We prove the existence of an upper bound on the asymptotic dimension of tree amalgamations of locally finite quasi-transitive connected graphs. This generalises a result of Dranishnikov for free products with amalgamation and a result of Tselekidis for HNN-extensions of groups to tree amalgamations of graphs. As a corollary, we obtain an upper bound on the asymptotic dimension of a multi-ended quasi-transitive locally finite graph based on any of their factorisations.
Keywords
Cite
@article{arxiv.1912.02683,
title = {Asymptotic dimension of multi-ended quasi-transitive graphs},
author = {Matthias Hamann},
journal= {arXiv preprint arXiv:1912.02683},
year = {2019}
}
Comments
7 pages