Bulletin of the
Korean Mathematical Society BKMS

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