The Speed and Threshold of the Biased Hamilton Cycle Game

Noah Brustle, Sarah Clusiau, Vishnu V. Narayan +3

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}}}…