We show that the cop number of any graph on 18 or fewer vertices is at most 3. This answers a question posed by Andreae in 1986, as well as more recently by Baird et al. We also find all 3-cop-win graphs on 11 vertices, narrow down the possible 4-cop-win graphs on 19 vertices and make some progress on finding the minimum order of 3-cop-win planar graphs.

翻译：我们显示,18个或更少的脊椎上的任何图的警号最多为3个。 这回答了Andreae在1986年提出的问题,以及Baird等人最近提出的问题。 我们还在11个脊椎上发现了所有3个Cop-win图,缩小了19个脊椎上可能的4个Cop-win图,并在找到3个Cop-win平面图的最低顺序方面取得了一些进展。