4-cop-win graphs have at least 19 vertices [article]

Jérémie Turcotte, Samuel Yvon
2021 arXiv   pre-print
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.
arXiv:2006.02998v2 fatcat:ask75apbijhspd23s5illqhvwu