Winning Fast in Sparse Graph Construction Games
نویسندگان
چکیده
منابع مشابه
Winning Fast in Sparse Graph Construction Games
A Graph Construction Game is a Maker-Breaker game. Maker and Breaker take turns in choosing previously unoccupied edges of the complete graph KN . Maker’s aim is to claim a copy of a given target graph G while Breaker’s aim is to prevent Maker from doing so. In this paper we show that if G is a d-degenerate graph on n vertices and N > d2n, then Maker can claim a copy of G in at most d2n rounds....
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We consider unbiased Maker-Breaker games played on the edge set of the complete graph Kn on n vertices. Quite a few such games were researched in the literature and are known to be Maker’s win. Here we are interested in estimating the minimum number of moves needed for Maker in order to win these games. We prove the following results, for sufficiently large n: (1) Maker can construct a Hamilton...
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In numerous positional games the identity of the winner is easily determined. In this case one of the more interesting questions is not who wins but rather how fast can one win. These type of problems were studied earlier for Maker-Breaker games; here we initiate their study for unbiased Avoider-Enforcer games played on the edge set of the complete graph Kn on n vertices. For several games that...
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For the unbiased Maker-Breaker game, played on the hypergraph H, let τM (H) be the smallest integer t such that Maker can win the game within t moves (if the game is a Breaker’s win then set τM (H) = ∞). Similarly, for the unbiased Avoider-Enforcer game played on H, let τE(H) be the smallest integer t such that Enforcer can win the game within t moves (if the game is an Avoider’s win then set τ...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2008
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548308009401