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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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


Author: Michael Krivelevich
Journal: J. Amer. Math. Soc. 24 (2011), 125-131
MSC (2010): Primary 05-XX; Secondary 91-XX
Published electronically: August 31, 2010
MathSciNet review: 2726601
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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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Additional 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

DOI: http://dx.doi.org/10.1090/S0894-0347-2010-00678-9
PII: S 0894-0347(2010)00678-9
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.
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.