This paper considers the one-cop-moves game played on a graph. In this game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph's edges with perfect information about each other's positions. The goal of the cops is to capture the robber. At cops' turns, exactly one cop is allowed to move from his location to an adjacent vertex; at robber's turns, she is allowed to move from her location to an adjacent vertex or to stay still. We want to find the minimum number of cops to capture the robber. This number is known as the cop number. In this paper, we investigate the cop number of several classes of graphs, including graphs with treewidth at most 2, Halin graphs, and Cartesian product graphs. We also give a characterization of k-winnable graphs in the one-cop-moves game.

本文考虑了在图表上玩的单警游戏。在此游戏中，一组警察和强盗占据了图的顶点，并沿图的边缘交替移动，并获得了关于彼此位置的完美信息。警察的目标是捕获强盗。警察轮到时，正好允许一个警察从他的位置移动到相邻的顶点；强盗轮到她时，她可以从其位置移至相邻顶点或保持静止。我们想找到捕获劫匪的最少警察人数。该号码称为警察号码。在本文中，我们研究了几类图的cop数，包括树宽最大为2的图，Halin图和笛卡尔乘积图。我们还给出了k的表征单警动作游戏中的可赢图。