@article{Lee2012DiracsTF,
title={Dirac's theorem for random graphs},
author={Choongbum Lee and Benny Sudakov},
journal={Random Struct. Algorithms},
year={2012},
volume={41},
pages={293-305}
}

A classical theorem of Dirac from 1952 asserts that every graph on n vertices with minimum degree at least dn/2e 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 ofG(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… CONTINUE READING