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We show that with high probability we can build a Hamilton cycle after atmost $1.85 n$ rounds in a particular semi-random model. In this model, in oneround, we are given a {uniform random} $v\in[n]$ and then we can add an{arbitrary} edge $\{v,w\}$. Our result improves on $2.016 n$ in a recent paperof Gao, MacRury, and Pralat.

Hamilton cycles in a semi-random graph model