Title

Hamilton cycles in random geometric graphs

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

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