On the minimum order of k-cop-win graphs
Combinatorics
2013-08-14 v1
Abstract
We consider the minimum order graphs with a given cop number. 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 and Meyniel's conjecture on the asymptotic maximum value of the cop number of a connected graph.
Keywords
Cite
@article{arxiv.1308.2841,
title = {On the minimum order of k-cop-win graphs},
author = {William Baird and Andrew Beveridge and Anthony Bonato and Paolo Codenotti and Aaron Maurer and John McCauley and Silviya Valeva},
journal= {arXiv preprint arXiv:1308.2841},
year = {2013}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1110.0768