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June 2011 Hamilton cycles in random geometric graphs
József Balogh, Béla Bollobás, Michael Krivelevich, Tobias Müller, Mark Walters
Ann. Appl. Probab. 21(3): 1053-1072 (June 2011). DOI: 10.1214/10-AAP718

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

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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

Information

Published: June 2011
First available in Project Euclid: 2 June 2011

zbMATH: 1222.05235
MathSciNet: MR2830612
Digital Object Identifier: 10.1214/10-AAP718

Subjects:
Primary: 05C45 , 05C80 , 60D05

Keywords: Hamilton cycles , Random geometric graphs

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.21 • No. 3 • June 2011
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