Growth and isoperimetric profile of planar graphs

Details Growth and isoperimetric profile of planar graphs Growth and isoperimetric profile of planar graphs

2010-04-27

arxiv.org/abs/1004.4726v1

Mathematics

Metric Geometry

8 pages

Scientific paper

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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