2014/09/11 by Mikhail I. Ostrovskii, Ostrovskii, Mikhail I., David Rosenthal +1 · 3 citations
Mathematics · #05C83 #20F65 (Primary) 05C63 #46B85 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #math.CO #math.GR #math.MG #msc:05C63 #msc:05C83 #msc:20F65 #msc:46B85
paper · pdf · doi:10.48550/arxiv.1409.3287
arxiv created 2014/09/11 · arxiv updated 2014/09/12
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.