The critical bias for the Hamiltonicity game is (1+𝑜(1))𝑛/ln𝑛

Krivelevich, Michael

doi:10.1090/S0894-0347-2010-00678-9

The critical bias for the Hamiltonicity game is $(1+o(1))n/\ln n$
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by Michael Krivelevich;

J. Amer. Math. Soc. 24 (2011), 125-131

DOI: https://doi.org/10.1090/S0894-0347-2010-00678-9

Published electronically: August 31, 2010

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Abstract:

We prove that in the biased $(1:b)$ Hamiltonicity Maker-Breaker game, played on the edges of the complete graph $K_n$, Maker has a winning strategy for $b(n)\le \left (1-\frac {30}{\ln ^{1/4}n}\right )\frac {n}{\ln n}$, for all large enough $n$.

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