A hole in a graph is an induced cycle of length at least 4. We give a simple winning strategy for t-3 cops to capture a robber in the game of cops and robbers played in a graph that does not contain a hole of length at least t. This strengthens a theorem of Joret-Kaminski-Theis, who proved that t-2 cops have a winning strategy in such graphs. As a consequence of our bound, we also give an inequality relating the cop number and the Dilworth number of a graph.

中文翻译：

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没有长孔的图形的 Cop 数量

图中的一个洞是一个长度至少为 4 的诱导循环。 我们给出了一个简单的获胜策略，让 t-3 警察在警察游戏中抓住一个强盗，而强盗在一个不包含长度为 4 的洞的图中玩至少 t。这加强了 Joret-Kaminski-Theis 的定理，他证明了 t-2 警察在此类图中具有制胜策略。作为我们界限的结果，我们还给出了一个与图的 cop 数和 Dilworth 数相关的不等式。