Metric dimensions of minor excluded graphs and minor exclusion in groups
2015 ◽
Vol 25
(04)
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pp. 541-554
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Keyword(s):
A Minor
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An infinite graph Γ is minor excluded if there is a finite graph that is not a minor of Γ. 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, like ℤ3; (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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2015 ◽
Vol 25
(08)
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pp. 1275-1299
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Keyword(s):
1999 ◽
Vol 42
(3)
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pp. 611-620
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2009 ◽
Vol 19
(04)
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pp. 585-594
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2014 ◽
Vol 24
(05)
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pp. 609-653
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Keyword(s):
2019 ◽
Vol 8
(2S11)
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pp. 4005-4008
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