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Counting 5‐connected planar triangulations
Author(s) -
Gao Zhicheng J.,
Wanless Ian M.,
Wormald Nicholas C.
Publication year - 2001
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.1021
Subject(s) - combinatorics , mathematics , planar graph , planar , graph , enhanced data rates for gsm evolution , planar straight line graph , discrete mathematics , 1 planar graph , line graph , computer science , telecommunications , computer graphics (images)
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