On the minimum order of $k$-cop win graphs

Authors

  • William Baird
  • Andrew Beveridge Macalester College
  • Anthony Bonato
  • Paolo Codenotti
  • Aaron Maurer
  • John McCauley
  • Silviya Valeva

DOI:

https://doi.org/10.11575/cdm.v9i1.62207

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 $k$ and Meyniel's conjecture on the asymptotic maximum value of the cop number of a connected graph.

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Published

2014-08-31

Issue

Vol. 9 No. 1 (2014)

Section

Articles

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