Jérémie Turcotte, Samuel Yvon
Published 2020-06-04Version 1
We show that the cop number of any graph on 18 or fewer vertices is at most 3. This answers a specific case of a question posed by Baird et al. on the minimum order of 4-cop-win graphs, first appearing in 2011. We also find all 3-cop-win graphs on 11 vertices, narrow down the possible 4-cop-win graphs on 19 vertices and get some progress on finding the minimum order of 3-cop-win planar graphs.
Comments: 27 pages, 9 figures. Data and code available at https://www.jeremieturcotte.com/research/min4cops/ . We are open to comments and are happy to help anyone understand the code
Variations on Cops and Robbers
The Cop Number of Graphs with Forbidden Induced Subgraphs
On the cop number of graphs of high girth
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