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The distribution of the maximum degree of a random graph

https://doi.org/10.1016/0012-365X(80)90054-0Get rights and content
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Abstract

Consider random graphs with n labelled vertices in which the edges are chosen independently and with a fixed probability p, 0<p<1. Let y be a fixed real number, q=1−p, and denote by Δ the maximum degree. Then PA⩽pn+(2pqn log n)121−log log n4 log nlog,(2π12)2 log n+y2 log n∼e-e-y∑m−1k=0e-kyk!

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