Open AccessGrowth and isoperimetric profile of planar graphs
Author(s) -
Itaï Benjamini,
Panos Papasoglu
Publication year - 2011
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-2011-10810-4
Subject(s) - algorithm , artificial intelligence , computer science
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