The Speed and Threshold of the Biased Perfect Matching Game

Abstract

We show that Maker wins the Maker-Breaker perfect matching game in $\frac{n}{2}+o(n)$ turns when the bias is at least $\frac{n}{\log n}-\frac{f(n)n}{(\log n{)}^{5/4}}$, for any $f$ going to infinity with $n$ and $n$ sufficiently large (in terms of $f$).

13 pages, 1 figure

Cited by in corpus (1)

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