## 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 $n$.## References

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## Bibliographic Information

**Michael Krivelevich**- Affiliation: School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
- Email: krivelev@post.tau.ac.il
- Received by editor(s): October 26, 2009
- Received by editor(s) in revised form: March 9, 2010
- Published electronically: August 31, 2010
- Additional Notes: This research was supported in part by a USA-Israel BSF grant, by a grant from the Israel Science Foundation, and by a Pazy Memorial Award.
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**24**(2011), 125-131 - MSC (2010): Primary 05-XX; Secondary 91-XX
- DOI: https://doi.org/10.1090/S0894-0347-2010-00678-9
- MathSciNet review: 2726601