Michael Krivelevich, Benny Sudakov
Published 2001-06-10Version 1
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.
On the variational problem for upper tails in sparse random graphs
On the number of Hamilton cycles in sparse random graphs
Optimal packings of Hamilton cycles in sparse random graphs
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