# Connectivity threshold for Bluetooth graphs

Abstract : We study the connectivity properties of random Bluetooth graphs that model certain "ad hoc" wireless networks. The graphs are obtained as "irrigation subgraphs" of the well-known random geometric graph model. There are two parameters that control the model: the radius $r$ that determines the "visible neighbors" of each node and the number of edges $c$ that each node is allowed to send to these. The randomness comes from the underlying distribution of data points in space and from the choices of each vertex. We prove that no connectivity can take place with high probability for a range of parameters $r, c$ and completely characterize the connectivity threshold (in $c$) for values of $r$ close the critical value for connectivity in the underlying random geometric graph.
Type de document :
Article dans une revue
Random Structures and Algorithms, Wiley, 2014, 44, pp.45-66. 〈10.1002/rsa.20459〉
Domaine :
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https://hal.inria.fr/hal-00773366
Contributeur : Nicolas Broutin <>
Soumis le : dimanche 13 janvier 2013 - 16:06:07
Dernière modification le : vendredi 25 mai 2018 - 12:02:03

### Citation

Nicolas Broutin, Luc Devroye, Nicolas Fraiman, Gábor Lugosi. Connectivity threshold for Bluetooth graphs. Random Structures and Algorithms, Wiley, 2014, 44, pp.45-66. 〈10.1002/rsa.20459〉. 〈hal-00773366〉

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