论文标题
$ k_n $的服务员 - 客户游戏中的快速策略
Fast Strategies in Waiter-Client Games on $K_n$
论文作者
论文摘要
在某些HyperGraph $（x，\ Mathcal {f}）$上播放服务员 - 客户游戏，其中$ \ Mathcal {f} $表示获胜的家族。对于某些偏见$ b $，在这样的游戏服务员为客户提供$ b+1 $元素的每轮$ x $的元素中，其余的元素在侍应生中为自己声称自己。如果她强迫客户索取从$ \ Mathcal {f} $索取所有获胜的元素，则像这样的服务员赢得了游戏。在本文中，我们研究了在完整图的边缘播放的几个服务员 - 客户游戏的快速策略，即$ x = e（k_n）$，其中获胜套装是完美的匹配，汉密尔顿周期，庞然大物图，固定的跨越树木或给定图形的因素。
Waiter-Client games are played on some hypergraph $(X,\mathcal{F})$, where $\mathcal{F}$ denotes the family of winning sets. For some bias $b$, during each round of such a game Waiter offers to Client $b+1$ elements of $X$, of which Client claims one for himself while the rest go to Waiter. Proceeding like this Waiter wins the game if she forces Client to claim all the elements of any winning set from $\mathcal{F}$. In this paper we study fast strategies for several Waiter-Client games played on the edge set of the complete graph, i.e. $X=E(K_n)$, in which the winning sets are perfect matchings, Hamilton cycles, pancyclic graphs, fixed spanning trees or factors of a given graph.
