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 κ such that almost every κ-connected graph has a Hamilton cycle.
Citation
József Balogh. Béla Bollobás. Michael Krivelevich. Tobias Müller. Mark Walters. "Hamilton cycles in random geometric graphs." Ann. Appl. Probab. 21 (3) 1053 - 1072, June 2011. https://doi.org/10.1214/10-AAP718
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