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Growth and isoperimetric profile of planar graphs

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arxiv 1004.4726 v1 pith:QQGWYLBB submitted 2010-04-27 math.MG

Itai Benjamini , Panos Papasoglu This is my paper · ORCID
classification math.MG
keywords omegaplanarsubsetboundaryconstantdomaineveryfunction
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Let G be a planar graph such that the volume function of G satisfies V(2n)< CV(n) for some constant C > 0. Then for every vertex v of G and integer n, there is a domain \Omega such that B(v,n) \subset \Omega, \Omega \subset B(v, 6n) and the size of the boundary of \Omega is at most order n.

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