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arXiv · 2208.00255

Hamilton cycles in a semi-random graph model

Alan Frieze·Gregory B. Sorkin
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Abstract

We show that with high probability we can build a Hamilton cycle after at most $1.85 n$ rounds in a particular semi-random model. In this model, in one round, 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 paper of Gao, MacRury, and Pralat.

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Alan Frieze, Gregory B. Sorkin. 2022-08-15. Hamilton cycles in a semi-random graph model. https://arxiv.org/abs/2208.00255

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