Hamilton cycles in random geometric graphs

Authors

József Balogh, University of Illinois Urbana-ChampaignFollow
Béla Bollobás, Faculty of MathematicsFollow
Michael Krivelevich, Tel Aviv University
Tobias Müller, Centrum Wiskunde & Informatica
Mark Walters, Queen Mary University of LondonFollow

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. © Institute of Mathematical Statistics, 2011.

Publication Title

Annals of Applied Probability

Recommended Citation

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