Geodesic
The critical bias for the Hamiltonicity game is (1+𝑜(1))𝑛/ln𝑛
Krivelevich, Michael1
1 School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Journal of the American Mathematical Society, Tome 24 (2011) no. 1, pp. 125-131

Voir la notice de l'article provenant de la source American Mathematical Society

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 $n$.
DOI : 10.1090/S0894-0347-2010-00678-9

Krivelevich, Michael 1

1 School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel 
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Krivelevich, Michael. The critical bias for the Hamiltonicity game is (1+𝑜(1))𝑛/ln𝑛. Journal of the American Mathematical Society, Tome 24 (2011) no. 1, pp. 125-131. doi: 10.1090/S0894-0347-2010-00678-9

[1] Beck, Jã³Zsef Random graphs and positional games on the complete graph 1985 7 13

[2] Beck, Jã³Zsef Combinatorial games 2008

[3] Bollobã¡S, Bã©La Random graphs 2001

[4] Bollobã¡S, B., Papaioannou, A. A biased Hamiltonian game Congr. Numer. 1982 105 115

[5] Chvã¡Tal, V., Erdå‘S, P. Biased positional games Ann. Discrete Math. 1978 221 229

[6] Gebauer, Heidi, Szabã³, Tibor Asymptotic random graph intuition for the biased connectivity game Random Structures Algorithms 2009 431 443

[7] Hefetz, Dan, Krivelevich, Michael, Stojakoviä‡, Miloå¡, Szabã³, Tibor Fast winning strategies in Maker-Breaker games J. Combin. Theory Ser. B 2009 39 47

[8] Hefetz, Dan, Stich, Sebastian On two problems regarding the Hamiltonian cycle game Electron. J. Combin. 2009

[9] Krivelevich, Michael, Szabã³, Tibor Biased positional games and small hypergraphs with large covers Electron. J. Combin. 2008

[10] Pã³Sa, L. Hamiltonian circuits in random graphs Discrete Math. 1976 359 364

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