An O(n) time algorithm for finding Hamilton cycles with high probability

We design a randomized algorithm that finds a Hamilton cycle in $\mathcal{O}(n)$ time with high probability in a random graph $G_{n,p}$ with edge probability $p\ge C\log n\mathrm{/}n$. This closes a gap left open in a seminal paper by Angluin and Valiant from 1979.