Counting 5-connected planar triangulations

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Abstract

Let t n be the number of rooted 5-connected planar triangulations with 2n faces. We find t n exactly for small n, as well as an asymptotic formula for n → ∞. Our results are found by compositions of lower connectivity maps whose faces are triangles or quadrangles. We also find the asymptotic number of cyclically 5-edge connected cubic planar graphs.

Original languageEnglish
Pages (from-to)18-35
Number of pages18
JournalJournal of Graph Theory
Volume38
Issue number1
DOIs
Publication statusPublished - Sep 2001
Externally publishedYes

Keywords

  • 5-connected
  • Cubic graph
  • Enumeration
  • Planner map
  • Triangulation

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