A classical theorem of Dirac from 1952 asserts that every graph on n vertices with minimum degree at least  \documentclass{article} \usepackage{mathrsfs} \usepackage{amsmath} \pagestyle{empty} \begin{document} \begin{align*}\left\lceil n/2 \right\rceil\end{align*} \end{document} **image** is Hamiltonian. In this paper we extend this result to random graphs. Motivated by the study of resilience of random graph properties we prove that if p ≫ log n/n, then a.a.s. every subgraph of G(n,p) with minimum degree at least (1/2 + o (1))np is Hamiltonian. Our result improves on previously known bounds, and answers an open problem of Sudakov and Vu. Both, the range of edge probability p and the value of the constant 1/2 are asymptotically best possible. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012#R##N##R##N#(Supported by NSF CAREER grant, NSF grant DMS-1101185 and USA-Israel BSF grant.)
['Choongbum Lee', 'Benny Sudakov']
Dirac's theorem for random graphs