A note on the distribution of the extreme degrees of a random graph via the Stein-Chen method

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2204.05881.pdf (133.68 KB)

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https://arxiv.org/abs/2204.05881

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http://hdl.handle.net/11603/24771
 https://doi.org/10.48550/arXiv.2204.05881

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UMBC Mathematics and Statistics Department
UMBC Faculty Collection

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https://orcid.org/0000-0003-2888-674X

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2022-04-13

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journal articles
preprints
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Abstract

We offer an alternative proof, using the Stein-Chen method, of Bollobás' theorem concerning the distribution of the extreme degrees of a random graph. The same method also applies in a more general setting where the probability of every pair of vertices being connected by edges depends on the number of vertices.