The Speed and Threshold of the Biased Hamilton Cycle Game
Noah Brustle, Sarah Clusiau, Vishnu V. Narayan, Ndiamé Ndiaye, B·2020-12-08·via math.CO updates on arXiv.org
We show that there is a constant C such that for any $b<\frac{n}{\ln{n}}-\frac{Cn}{(\ln{n})^{3/2}}$, Maker wins the Maker-Breaker Hamilton cycle game in $n+\frac{Cn}{\sqrt{\ln{n}}}$ steps.