Biased positional games on matroids
نویسندگان
چکیده
منابع مشابه
Security games on matroids
Two players, the Defender and the Attacker play the following game. A matroid M = (S,I ), a weight function d : S→ R+ and a cost function c : S→ R are given. The Defender chooses a base B of the matroid M and the Attacker chooses an element s ∈ S of the ground set. In all cases, the Attacker pays the Defender the cost of attack c(s). Besides that, if s ∈ B then the Defender pays the Attacker th...
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We prove that in the biased (1 : b) Hamiltonicity and k-connectivity MakerBreaker games (k > 0 is a constant), played on the edges of the complete graph Kn, Maker has a winning strategy for b ≤ (log 2− o(1))n/ log n. Also, in the biased (1 : b) Avoider-Enforcer game played on E(Kn), Enforcer can force Avoider to create a Hamilton cycle when b ≤ (1− o(1))n/ log n. These results are proved using ...
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Two new versions of the so-called Maker-Breaker Positional Games are defined by József Beck. In these variants Picker takes unselected pair of elements and Chooser keeps one of these elements and gives back the other to Picker. In the Picker-Chooser version Picker is Maker and Chooser is Breaker, while the roles are swapped in the Chooser-Picker version. It seems that both the Picker-Chooser an...
متن کاملPositional games on random graphs
We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability pF for the existence of Maker’s strategy to claim a member of F in the unbiased game played on the edges of random graph G(n, p), for various target families F of winning sets. More generally, for each probability above this threshold we study the smallest bias...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2005
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2003.12.015