THe largest eigenvalue of sparse random graphs
组合数学
2007-05-23 v1 概率论
摘要
We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n,p) satisfies almost surely: \lambda_1(G)=(1+o(1))max{\sqrt{\Delta},np}, where \Delta is a maximal degree of G, and the o(1) term tends to zero as max{\sqrt{\Delta},np} tends to infinity.
引用
@article{arxiv.math/0106066,
title = {THe largest eigenvalue of sparse random graphs},
author = {Michael Krivelevich and Benny Sudakov},
journal= {arXiv preprint arXiv:math/0106066},
year = {2007}
}