论文标题
制造商在挖掘机上
Maker Breaker on Digraphs
论文作者
论文摘要
我们研究了在完整的Digraph $ \ vec {k} _n $上玩过的两个偏见的破坏者游戏。在强大的连接游戏中，Maker希望建立一个牢固的连接子图。我们确定该游戏的渐近最佳偏见。 $ \ frac {n} {\ log n} $。在汉密尔顿游戏中，制造商希望建立一个汉密尔顿子图。我们确定该游戏的渐近最佳偏见，最高为恒定因素。
We study two biassed Maker-Breaker games played on the complete digraph $\vec{K}_n$. In the strong connectivity game, Maker wants to build a strongly connected subgraph. We determine the asymptotic optimal bias for this game viz. $\frac{n}{\log n}$. In the Hamiltonian game, Maker wants to build a Hamiltonian subgraph. We determine the asymptotic optimal bias for this game up to a constant factor.
