A random Bernoulli subset of any finite group of order N has VC-dimension (1+o(1)) log_r N with high probability, where r = 1/min(p,1-p).
The chromatic number of random Cayley graphs
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The VC-dimension of random subsets of finite groups
A random Bernoulli subset of any finite group of order N has VC-dimension (1+o(1)) log_r N with high probability, where r = 1/min(p,1-p).