Gale-Ryser and Fulkerson–Chen–Anstee checks for degree sequences.

[dgleich]

Now that we have Havel Hakimi, it'd be good to have analog for the bipartite graph and directed graph.
(https://en.wikipedia.org/wiki/Gale%E2%80%93Ryser_theorem)
and
https://en.wikipedia.org/wiki/Fulkerson%E2%80%93Chen%E2%80%93Anstee_theorem
Although the second seems very close to the former.