I need a list of $\Sigma_2^p$ complete languages. There are two such problems listed in the Complexity Zoo, namely:
Another basic $\Sigma_2^p$ complete problem:
However, I am hopefully looking for a problem which makes use of graphs (e.g. a clique related problem).
Marcus Schaefer and Chris Umans have a nice Garey-and-Johnson-esque survey of complete problems in the polynomial hierarchy.
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