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.

Publication Title

Annals of Applied Probability