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2014 | OriginalPaper | Chapter

9. The Largest Clique in a Random Graph and Applications to Tampering Detection and Ramsey Theory

Author : Ross G. Pinsky

Published in: Problems from the Discrete to the Continuous

Publisher: Springer International Publishing

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Abstract

A finite graph G is a pair (V, E), where V is a finite set of vertices and E is a subset of V (2), the set of unordered pairs of elements of V. The elements of E are called edges. (This is what graph theorists call a simple graph.

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previous chapter The Hardy–Ramanujan Theorem on the Number of Distinct Prime Divisors
next chapter The Phase Transition Concerning the Giant Component in a Sparse Random Graph: A Theorem of Erdős and Rényi
Literature
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Alon, N., Spencer, J.: The Probabilistic Method, 3rd edn. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, Hoboken (2008)CrossRefMATH
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Alon, N., Krivelevich, M., Sudakov, B.: Finding a large hidden clique in a random graph. In: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, CA, 1998), pp. 594–598. ACM, New York (1998)
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Bollobás, B.: Modern Graph Theory. Graduate Texts in Mathematics, vol. 184. Springer, New York (1998)
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Bollobás, B.: Random Graphs, 2nd edn. Cambridge Studies in Advanced Mathematics, vol. 73. Cambridge University Press, Cambridge (2001)
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22.
Graham, R., Rothschild, B., Spencer, J.: Ramsey Theory, 2nd edn. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York (1990)MATH
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Metadata
Title
The Largest Clique in a Random Graph and Applications to Tampering Detection and Ramsey Theory
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_9