The critical bias for the Hamiltonicity game is n/ lnn
نویسنده
چکیده
We prove that in the biased (1 : b) Hamiltonicity Maker-Breaker game, played on the edges of the complete graph Kn, Maker has a winning strategy for b(n) ≤ ( 1− 30 ln n ) n lnn , for all large enough n.
منابع مشابه
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In this paper we analyze biased Maker-Breaker games and Avoider-Enforcer games, both played on the edge set of a random board G ∼ G(n, p). In Maker-Breaker games there are two players, denoted by Maker and Breaker. In each round, Maker claims one previously unclaimed edge of G and Breaker responds by claiming b previously unclaimed edges. We consider the Hamiltonicity game, the perfect matching...
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