Hyperbolic notions on a planar graph of bounded face degree
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1305-1319
https://doi.org/10.4134/BKMS.2015.52.4.1305
Published online July 31, 2015
Byung-Geun Oh
Hanyang University
Abstract : We study the relations between strong isoperimetric inequalities and Gromov hyperbolicity on planar graphs, and give an alternative proof for the following statement: if a planar graph of bounded face degree satisfies a strong isoperimetric inequality, then it is Gromov hyperbolic. This theorem was formerly proved in the author's paper from 2014 \cite{Oh2} using combinatorial methods, while geometric approach is used in the present paper.
Keywords : planar graph, strong isoperimetric inequality, Gromov hyper\-bolicity
MSC numbers : Primary 05C10, 53C23; Secondary 53C45, 05B45, 52C20
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