  We consider sampling and enumeration problems for Markov equivalence classes.
We create and analyze a Markov chain for uniform random sampling on the DAGs
inside a Markov equivalence class. Though the worst case is exponentially slow
mixing, we find a condition on the Markov equivalence class for polynomial time
mixing. We also investigate the ratio of Markov equivalence classes to DAGs and
a Markov chain of He, Jia, and Yu for random sampling of sparse Markov
equivalence classes.
