Metric dimensions of minor excluded graphs and minor exclusion in groups

Mikhail I. Ostrovskii; David Rosenthal

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arXiv · 1409.3287

Metric dimensions of minor excluded graphs and minor exclusion in groups

Mikhail I. Ostrovskii·David Rosenthal

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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.

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BibTeX RIS

Mikhail I. Ostrovskii, David Rosenthal. 2014-09-11. Metric dimensions of minor excluded graphs and minor exclusion in groups. https://arxiv.org/abs/1409.3287

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