  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.
