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On the probability of the existence of fixed-size components in random geometric graphs

Part of: Combinatorial probability Discrete mathematics in relation to computer science

Published online by Cambridge University Press:  01 July 2016

J. Díaz ,
D. Mitsche  and
X. Pérez-Giménez
J. Díaz*
Affiliation:
Universitat Politècnica de Catalunya
D. Mitsche*
Affiliation:
ETH Zürich
X. Pérez-Giménez*
Affiliation:
Universitat Politècnica de Catalunya
*
∗ Postal address: Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, UPC, 08034 Barcelona, Spain.
∗∗∗ Postal address: Institut für Theoretische Informatik, ETH Zürich, 8092 Zürich, Switzerland. Email address: dmitsche@inf.ethz.ch
∗ Postal address: Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, UPC, 08034 Barcelona, Spain.
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Abstract

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In this work we give precise asymptotic expressions for the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

Keywords

Random geometric graphconnectivity thresholdcomponent size

MSC classification

Primary: 68R10: Graph theory (including graph drawing)
Secondary: 60C05: Combinatorial probability
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 41 , Issue 2 , June 2009 , pp. 344 - 357
Copyright
Copyright © Applied Probability Trust 2009 

References

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