Discrete MathematicsVolume 32, Issue 2, 1980, Pages 201-203NoteThe distribution of the maximum degree of a random graphAuthor links open overlay panelBéla BollobásShow moreShareCitehttps://doi.org/10.1016/0012-365X(80)90054-0Get rights and contentUnder an Elsevier user licenseopen archiveAbstractConsider 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 n−log,(2π12)2 log n+y2 log n∼e-e-y∑m−1k=0e-kyk!Previous article in issueNext article in issueRecommended articlesCited by (0)Copyright © 1980 Published by Elsevier B.V.