Recently the matcher game was introduced. In this game, two players create a maximal matching by one player repeatedly choosing a vertex and the other player choosing a $K_2$ containing that vertex. One player tries to minimize the result and the other to maximize the this http URL this paper we propose a generalization of this game where $K_2$ is replaced by a general graph $F$. We focus here on the case of $F=P_3$. We provide some general results and lower bounds for the game, investigate the graphs where the game ends with all vertices taken, and calculate the value for some specific families of graphs.

中文翻译：

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广义匹配游戏

最近推出了匹配器游戏。在这个游戏中，两个玩家通过一个玩家重复选择一个顶点而另一个玩家选择包含该顶点的 $K_2$ 来创建最大匹配。一个玩家试图最小化结果，另一个玩家试图最大化这个 http URL。本文我们提出了这个游戏的泛化，其中 $K_2$ 被一个通用图 $F$ 代替。我们这里关注的是 $F=P_3$ 的情况。我们为游戏提供了一些一般结果和下界，研究了游戏结束时所有顶点都被占用的图，并计算了一些特定图族的值。