We consider a variant of Cops and Robbers in which the robber may traverse as many edges as he likes in each turn, with the constraint that he cannot pass through any vertex occupied by a cop. We study this model on several classes of grid-like graphs. In particular, we determine the cop numbers for two-dimensional Cartesian grids and tori up to an additive constant, and we give asymptotic bounds for the cop numbers of higher-dimensional grids and hypercubes.

中文翻译：

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在网格上捕捉快速强盗

我们考虑 Cops and Robbers 的一种变体，其中强盗可以在每一轮中遍历任意多的边，约束条件是他不能通过被警察占据的任何顶点。我们在几类网格状图上研究了这个模型。特别是，我们确定二维笛卡尔网格和圆环的 cop 数直到一个加性常数，并且我们给出了高维网格和超立方体的 cop 数的渐近边界。