volume 28, issue 3, P313-330 2002
DOI: 10.1007/s00454-002-0694-2
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Abstract: Let G be an infinite locally finite plane graph with one end and let H be a finite plane subgraph of G. Denote by a(H ) the number of finite faces of H and by l(∂ H ) the number of the edges of H that are on the boundary of the infinite face or a finite face not in H . Define the isoperimetric constant h(G) to be inf H l(∂ H )/a(H ) and define the isoperimetric constant h(δ) to be inf G h(G)where the infimum is taken over all infinite locally finite plane graphs G having minimum degree δ and exactly one end. …

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