On the minimum order of $k$-cop win graphs
نویسندگان
چکیده
We consider the minimum order graphs with a given cop number k, and we focus especially on the cases k = 2, 3. We prove that the minimum order of a connected graph with cop number 3 is 10, and show that the Petersen graph is the unique isomorphism type of graph with this property. We provide the results of a computational search on the cop number of all graphs up to and including order 10. A relationship is presented between the minimum order of graph with cop number k and Meyniel’s conjecture on the asymptotic maximum value of the cop number of a connected graph.
منابع مشابه
Almost all k-cop-win graphs contain a dominating set of cardinality k
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عنوان ژورنال:
- Contributions to Discrete Mathematics
دوره 9 شماره
صفحات -
تاریخ انتشار 2014