Growth and isoperimetric profile of planar graphs

DOI10.1090/S0002-9939-2011-10810-4zbMath1241.53035arXiv1004.4726MaRDI QIDQ3103284

Itai Benjamini, Panos Papasoglu

Publication date: 7 December 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.4726

zbMATH Keywords

planar graphisoperimetric profilelocally finite graph

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (7)

Simple random walk on the uniform infinite planar quadrangulation: Subdiffusivity via pioneer points ⋮ Symmetry breaking in two-dimensional square grids: persistence and failure of the dimensional crossover ⋮ Separation profile, isoperimetry, growth and compression ⋮ Non-existence of annular separators in geometric graphs ⋮ Triangulations of uniform subquadratic growth are quasi-trees ⋮ On planar graphs of uniform polynomial growth ⋮ Conformal growth rates and spectral geometry on distributional limits of graphs

Cites Work

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• Recurrence of distributional limits of finite planar graphs
• A short proof that a subquadratic isoperimetric inequality implies a linear one
• A view from infinity of the uniform infinite planar quadrangulation
• Quantum Geometry
• Cheeger constants of surfaces and isoperimetric inequalities

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