Matteo García asks how to randomly sample degeneracy orderings of graphs (start with $k=1$ and at each step remove a vertex of degree at most $k$, or increase $k$ when no such vertex remains): cstheory.stackexchange.com/q/4

I think this question deserves more attention. My intuition is that it's hard (for instance it might be $\#\mathsf{P}$-complete to count degeneracy orderings of trees) but I don't see how to prove it.

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