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GROWTH AND ISOPERIMETRIC PROFILE OF PLANAR GRAPHS

Abstract:
Let Γ be a planar graph such that the volume function of Γ satisfies V(2n) ≤ CV(n) for some constant C > 0. Then for every vertex v of Γ and n ∈ N, there is a domain Ω such that B(v, n) ⊂ Ω, ∂Ω ⊂ B(v, 6n) and |∂Ω|{succeeds above almost equal to}. © 2011 American Mathematical Society.
Publication status:
Published

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Journal:
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume:
139
Issue:
11
Pages:
4105-4111
Publication date:
2011-11-01
DOI:
EISSN:
1088-6826
ISSN:
0002-9939
Source identifiers:
191458
Language:
English
Pubs id:
pubs:191458
UUID:
uuid:4ec4a095-0560-45ef-8e3a-60f0828b96c6
Local pid:
pubs:191458
Deposit date:
2012-12-19

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