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Deviation inequality for the number of k-cycles in a random graph

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Wuhan University Journal of Natural Sciences

Abstract

We study the number of k-cycles in a random graph G(n, p). We estimate the probability that a random graph contains more k-cycles than expected. In this case, the usual martingale inequality with bounded difference is not effective. By constructing a variable that approximates to the number of k-cycles in a random graph and using a new and extensive martingale inequality, we get the results in this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China

    Yanqing Wang & Fuqing Gao

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  1. Yanqing Wang
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  2. Fuqing Gao
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Correspondence to Fuqing Gao.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China (10571139)

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Wang, Y., Gao, F. Deviation inequality for the number of k-cycles in a random graph. Wuhan Univ. J. Nat. Sci. 14, 11–13 (2009). https://doi.org/10.1007/s11859-009-0103-2

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  • DOI: https://doi.org/10.1007/s11859-009-0103-2

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