Counting 5-connected planar triangulations

✍ Scribed by Zhicheng J. Gao; Ian M. Wanless; Nicholas C. Wormald

• Book ID: 102342579
• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 203 KB
• Volume: 38
• Category: Article
• ISSN: 0364-9024
• DOI: 10.1002/jgt.1021

✦ Synopsis

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