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Partitions with Restricted Summands or “the Money Changing Problem” Read chapter Read first chapter

2014 | OriginalPaper | Chapter

10. The Phase Transition Concerning the Giant Component in a Sparse Random Graph: A Theorem of Erdős and Rényi

Author : Ross G. Pinsky

Published in: Problems from the Discrete to the Continuous

Publisher: Springer International Publishing

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Abstract

Let \(G_{n}(p_{n}) = ([n],E_{n}(p_{n}))\) denote the Erdős–Rényi graph of size n which was introduced in Chap. 9. As in Chap. 9, the generic notation P for probability and E for expectation will be used in this chapter.

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previous chapter The Largest Clique in a Random Graph and Applications to Tampering Detection and Ramsey Theory
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Durrett, R.: Probability: Theory and Examples, 4th edn. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge (2010)CrossRef
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Erdős, P., Rényi, A.: On the evolution of random graphs. Magyar Tud. Akad. Mat. Kutató Int. Közl 5, 17–61 (1960)
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Harris, T.: The Theory of Branching Processes, corrected reprint of the 1963 original [Springer, Berlin]. Dover Publications, Inc., Mineola (2002)
Metadata
Title
The Phase Transition Concerning the Giant Component in a Sparse Random Graph: A Theorem of Erdős and Rényi
Author
Ross G. Pinsky
Copyright Year
2014
Book
Problems from the Discrete to the Continuous

Print ISBN: 978-3-319-07964-6

Electronic ISBN: 978-3-319-07965-3

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-319-07965-3_10