### Abstract

Let T_{n} be a 3‐connected n‐vertex planar triangulation chosen uniformly at random. Then the number of vertices in the largest 4‐connected component of T_{n} is asymptotic to n/2 with probability tending to 1 as n → ∞. It follows that almost all 3‐connected triangulations with n vertices have a cycle of length at least n/2 + o(n).

Original language | English |
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Pages (from-to) | 273-285 |

Number of pages | 13 |

Journal | Random Structures & Algorithms |

Volume | 7 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1995 |

Externally published | Yes |

## Cite this

Bender, E. A., Richmond, L. B., & Wormald, N. C. (1995). Largest 4‐connected components of 3‐connected planar triangulations.

*Random Structures & Algorithms*,*7*(4), 273-285. https://doi.org/10.1002/rsa.3240070402