Hamilton cycles in random geometric graphs
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.
Annals of Applied Probability
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