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Jul 14, 2018 at 4:21 comment added Morteza Azad Thanks for your answer, Mohammad! I think by adding enough so-called pitfalls (which actually don't change the cop number of a graph) to your examples one may obtain graphs of size $\kappa$ and cop number $\lambda$ for any infinite cardinals $\kappa, \lambda$.
Jul 14, 2018 at 3:07 history answered Mohammad Golshani CC BY-SA 4.0