In this paper, we study the game of cops and robber on the class of graphs with no even hole (induced cycle of even length) and claw (a star with three leaves). The cop number of a graph $G$ is defined as the minimum number of cops needed to capture the robber. Here, we prove that the cop number of all claw-free even-hole-free graphs is at most two and, in addition, the capture time is at most $2n$ rounds, where $n$ is the number of vertices of the graph. Moreover, our results can be viewed as a first step towards studying the structure of claw-free even-hole-free graphs.

翻译：在本文中,我们研究了警察和强盗在无孔(偶数周期)和爪子(三叶之星)的图表类中玩弄的警察和强盗游戏。 图表的警号被定义为捕捉强盗所需的最低警察人数 $G美元。 在这里,我们证明所有无爪、无洞、无爪、无洞的图表的警号最多最多只有两个,此外,捕捉时间最多为2美元,其中1美元是图表的顶点数。 此外,我们的结果可以被视为研究无爪、无洞、无洞图表结构的第一步。