Hyperbolic notions on a planar graph of bounded face degree

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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 [12] using combinatorial methods, while geometric approach is used in the present paper.

Original languageEnglish
Pages (from-to)1305-1319
Number of pages15
JournalBulletin of the Korean Mathematical Society
Volume52
Issue number4
DOIs
StatePublished - 2015 Jul 29

Keywords

  • Gromov hyperbolicity
  • Planar graph
  • Strong isoperimetric inequality

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