Random-Player Maker-Breaker games

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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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Maker-breaker games on random geometric graphs

In a Maker-Breaker game on a graph G, Breaker and Maker alternately claim edges of G. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games played on random geometric graphs. For each of our four games we show that if we add edges between n points chosen uniformly at random in the unit square by order of ...

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Fast Strategies In Maker-Breaker Games Played on Random Boards

In this paper we analyze classical Maker-Breaker games played on the edge set of a sparse random board G ∼ Gn,p. We consider the Hamiltonicity game, the perfect matching game and the k-connectivity game. We prove that for p(n) ≥ polylog(n)/n, the board G ∼ Gn,p is typically such that Maker can win these games asymptotically as fast as possible, i.e. within n+ o(n), n/2 + o(n) and kn/2 + o(n) mo...

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Generating random graphs in biased Maker-Breaker games

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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ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2015

ISSN: 1077-8926

DOI: 10.37236/5032