Hamilton cycles in random geometric graphs

József Balogh; Béla Bollobás; Michael Krivelevich; Tobias Müller; Mark Walters

doi:10.1214/10-AAP718

Hamilton cycles in random geometric graphs

József Balogh, Béla Bollobás, Michael Krivelevich, Tobias Müller, Mark Walters

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1053-1072
Number of pages	20
Journal	Annals of Applied Probability
Volume	21
Issue number	3
DOIs	https://doi.org/10.1214/10-AAP718
State	Published - Jun 2011

Keywords

Hamilton cycles
Random geometric graphs

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/10-AAP718

Cite this

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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.",

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AB - 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.

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EP - 1072

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 3

ER -

Hamilton cycles in random geometric graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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