Maker-breaker games on random geometric graphs

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چکیده

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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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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 consider Maker-Breaker games, played on the edges of sparse graphs. For a given graph property P we seek a graph (board of the game) with the smallest number of edges on which Maker can build a subgraph that satisfies P. In this paper we focus on global properties. We prove the following results: 1) for the positive minimum degree game, there is a winning board with n vertices ...

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ژورنال

عنوان ژورنال: Random Structures & Algorithms

سال: 2014

ISSN: 1042-9832

DOI: 10.1002/rsa.20572