论文标题
在树上的触摸器隔离器游戏中的隔离器策略
A strategy for Isolator in the Toucher-Isolator game on trees
论文作者
论文摘要
在Toucher-Sisolator游戏中，Dowden，Kang，Mikalački和Stojaković，Toucher and Inalator交替地从图中声称具有优势，以至于触摸器的目标是触摸尽可能多的顶点，而隔离器的目标是隔离尽可能多的顶点，首先是触摸器。在带有$ n $顶点的树木中，他们表明恒星是隔离器的最佳选择，他们要求最合适的树。后来，Räty表明答案是$ N $顶点的路径。我们给出了一个简单的替代证明。确定隔离器应在何处玩的方法是通过分解两个玩家的每一步的收益和损失。
In the Toucher-Isolator game, introduced recently by Dowden, Kang, Mikalački and Stojaković, Toucher and Isolator alternately claim an edge from a graph such that Toucher aims to touch as many vertices as possible, while Isolator aims to isolate as many vertices as possible, where Toucher plays first. Among trees with $n$ vertices, they showed that the star is the best choice for Isolator and they asked for the most suitable tree for Toucher. Later, Räty showed that the answer is the path with $n$ vertices. We give a simple alternative proof of this result. The method to determine where Isolator should play is by breaking down the gains and losses in each move of both players.
