Counting 5-connected planar triangulations

  • Authors:

  • Zhicheng J. Gao;Ian M. Wanless;Nicholas C. Wormald

  • Affiliations:

  • Department of Mathematics and Statistics, Carleton University, Ottawa Canada K1S 5B6;Department of Mathematics and Statistics, University of Melbourne VIC 3010 Australia;Department of Mathematics and Statistics, University of Melbourne VIC 3010 Australia

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2001

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Abstract

Let tn be the number of rooted 5-connected planar triangulations with 2n faces. We find tn 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