论文标题
随机超图中的制造商突破游戏
Maker-Breaker Games on Random Hypergraphs
论文作者
论文摘要
在本文中，我们在随机的Hypraph $ h_ {n，s，p} $上研究了制造商 - 破坏者游戏，这是通过与概率$ p $独立保持每个优势的方式，从完整的$ s $绘制中获得。我们确定制造商财产赢得游戏的阈值概率是$ s $，基础超图的均匀性以及$ m $，$ b $，这是允许制造商和断路器的顶点数量。 此外，我们表明，根据这些$ m，b，s $，有两种类型的阈值：要么是制造商，要么是本地属性，阈值较弱，或者与随机超图的全局属性有关，阈值是半股。我们猜想，在后一种情况下，阈值实际上是尖锐的。
In this paper, we study Maker-Breaker games on the random hypergraph $H_{n,s,p}$, obtained from the complete $s$-graph by keeping every edge independently with probability $p$. We determine the threshold probability for the property of Maker winning the game as a function of $s$, the uniformity of the underlying hypergraph, as well as $m$, $b$, the number of vertices that Maker and Breaker are respectively allowed to pick each turn. In addition, we show that depending on those $m,b,s$, there are two types of thresholds: either being Maker-win is a local property and the threshold is weak, or it is related to global properties of the random hypergraph and the threshold is semi-sharp. We conjecture that in the latter case, the threshold is actually sharp.
