We study a new optimal stopping problem: Let G be a fixed graph with n vertices which become active on-line in time, one by another, in a random order. The active part of G is the subgraph induced by the active vertices. Find a stopping algorithm that maximizes the expected number of connected components of the active part of G. We prove that if G is a k-tree, then there is no asymptotically better algorithm than “wait until fraction of vertices”. The maximum expected number of connected components is equal to

中文翻译：

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图中许多连通分量的最佳停止

我们研究了一个新的最优停止问题：让G是一个固定的图，它有n个顶点，它们以随机顺序一个接一个地在线激活。G的活动部分是由活动顶点诱导的子图。找到一个停止算法，使G的活动部分的连接分量的预期数量最大化。我们证明，如果G是k树，那么没有比“等到顶点的分数”渐近更好的算法。连接组件的最大预期数量等于