# The phase transition in random graphs: A simple proof

@article{Krivelevich2013ThePT, title={The phase transition in random graphs: A simple proof}, author={Michael Krivelevich and Benny Sudakov}, journal={Random Structures \& Algorithms}, year={2013}, volume={43} }

The classical result of Erdős and Rényi asserts that the random graph G(n,p) experiences sharp phase transition around \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath}\pagestyle{empty}\begin{document}\begin{align*}p=\frac{1}{n}\end{align*} \end{document} – for any ε > 0 and \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath}\pagestyle{empty}\begin{document}\begin{align*}p=\frac{1-\epsilon}{n}\end{align*} \end{document}, all connected components of G(n,p) are…

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