Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T12:41:20.865Z Has data issue: false hasContentIssue false
  • English
  • Français

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

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

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: [email protected]
∗ Postal address: Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, UPC, 08034 Barcelona, Spain.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Bollobás, B. (2001). Random Graphs (Camb. Stud. Adv. Math. 73), 2nd edn. Cambridge University Press.Google Scholar
Dı´az, J., Petit, J. and Serna, M. (2001). A guide to concentration bounds. In Handbook of Randomized Computing, Vol. II, eds. Rajasekaran, S. et al., Kluwer, Dordrecht, pp. 457–507.Google Scholar
Gupta, P. and Kumar, P. R. (1999). Critical power for asymptotic connectivity in wireless networks. In Stochastic Analysis, Control, Optimization and Applications, Birkhäuser, Boston, MA, pp. 547–566.Google Scholar
Hekmat, R. (2006). Ad-hoc Networks: Fundamental Properties and Network Topologies, Springer, Dordrecht.Google Scholar
Penrose, M. (1997). The longest edge of the random minimal spanning tree. Ann. Appl. Prob. 7, 340–361.Google Scholar
Penrose, M. (2003). Random Geometric Graphs (Oxford Stud. Prob. 5). Oxford University Press.Google Scholar