# Hamilton cycles in random geometric graphs - Mathematics > Probability

Abstract: We prove that, in the Gilbert model for a random geometric graph, almostevery graph becomes Hamiltonian exactly when it first becomes 2-connected. Thisanswers a question of Penrose. We also show that in the k-nearest neighbormodel, there is a constant \kappa\ such that almost every \kappa-connectedgraph has a Hamilton cycle.

Author: József Balogh, Béla Bollobás, Michael Krivelevich, Tobias Müller, Mark Walters

Source: https://arxiv.org/