Random Cayley graphs on any group of order N have clique number O(log N log log N) with high probability, giving near-optimal Ramsey and self-complementary Cayley graphs.
Alon, Research problems, Discrete Math
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On the clique number of random Cayley graphs and related topics
Random Cayley graphs on any group of order N have clique number O(log N log log N) with high probability, giving near-optimal Ramsey and self-complementary Cayley graphs.