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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The critical bias for the Hamiltonicity game is $(1+o(1))n/\ln n$
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by Michael Krivelevich PDF
J. Amer. Math. Soc. 24 (2011), 125-131 Request permission


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:
  • 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:
  • MathSciNet review: 2726601