Metric dimensions of minor excluded graphs and minor exclusion in groups
Group Theory
2014-09-12 v1 Combinatorics
Metric Geometry
Abstract
An infinite graph G is minor excluded if there is a finite graph that is not a minor of G. We prove that minor excluded graphs have finite Assouad-Nagata dimension and study minor exclusion for Cayley graphs of finitely generated groups. Our main results and observations are: (1) minor exclusion is not a group property: it depends on the choice of generating set; (2) a group with one end has a generating set for which the Cayley graph is not minor excluded; (3) there are groups that are not minor excluded for any set of generators; (4) minor exclusion is preserved under free products; and (5) virtually free groups are minor excluded for any choice of finite generating set.
Keywords
Cite
@article{arxiv.1409.3287,
title = {Metric dimensions of minor excluded graphs and minor exclusion in groups},
author = {Mikhail I. Ostrovskii and David Rosenthal},
journal= {arXiv preprint arXiv:1409.3287},
year = {2014}
}