Counting 5‐connected planar triangulations

Abstract

Abstract Let t n be the number of rooted 5‐connected planar triangulations with 2 n 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. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 18–35, 2001