### Abstract

We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penrose. We also show that in the κ-nearest neighbor model, there is a constant κ such that almost every κ-connected graph has a Hamilton cycle.

Original language | English (US) |
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Pages (from-to) | 1053-1072 |

Number of pages | 20 |

Journal | Annals of Applied Probability |

Volume | 21 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2011 |

### Keywords

- Hamilton cycles
- Random geometric graphs

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

Balogh, J., Bollobás, B., Krivelevich, M., Müller, T., & Walters, M. (2011). Hamilton cycles in random geometric graphs.

*Annals of Applied Probability*,*21*(3), 1053-1072. https://doi.org/10.1214/10-AAP718