Walker-Breaker Games
نویسندگان
چکیده
We introduce and analyze the Walker-Breaker game, a variant of Maker-Breaker games where Maker is constrained to choose edges of a walk or path in a given graph G, with the goal of visiting as many vertices of the underlying graph as possible.
منابع مشابه
Random-Player Maker-Breaker games
In a (1 : b) Maker-Breaker game, one of the central questions is to find the maximal value of b that allows Maker to win the game (that is, the critical bias b∗). Erdős conjectured that the critical bias for many Maker-Breaker games played on the edge set of Kn is the same as if both players claim edges randomly. Indeed, in many Maker-Breaker games, “Erdős Paradigm” turned out to be true. There...
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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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We present a general approach connecting biased Maker-Breaker games and problems about local resilience in random graphs. We utilize this approach to prove new results and also to derive some known results about biased Maker-Breaker games. In particular, we show that for b = Θ( n lnn), playing a (1 : b) game on E(Kn), Maker can build a graph which contains copies of all spanning trees having ma...
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 29 شماره
صفحات -
تاریخ انتشار 2015