Hamilton cycles in random geometric graphs
Probability
2012-11-09 v2 Combinatorics
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 k-nearest neighbor model, there is a constant \kappa\ such that almost every \kappa-connected graph has a Hamilton cycle.
Keywords
Cite
@article{arxiv.0905.4650,
title = {Hamilton cycles in random geometric graphs},
author = {József Balogh and Béla Bollobás and Michael Krivelevich and Tobias Müller and Mark Walters},
journal= {arXiv preprint arXiv:0905.4650},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/10-AAP718 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)