Almost all cop-win graphs contain a universal vertex

We consider cop-win graphs in the binomial random graph G(n,1/2). We prove that almost all cop-win graphs contain a universal vertex. From this result, we derive that the asymptotic number of labelled cop-win graphs of order n is equal to (1+o(1))n2^n^^^2^/^2^-^3^n^/^2^+^1.

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