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arXiv · 0905.4650

Hamilton cycles in random geometric graphs

József Balogh·Béla Bollobás·Michael Krivelevich·Tobias Müller·Mark Walters
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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.

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József Balogh, Béla Bollobás, Michael Krivelevich, Tobias Müller, Mark Walters. 2009-05-28. Hamilton cycles in random geometric graphs. https://doi.org/10.1214/10-aap718

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