I have been reading through the history of the Havel-Hakimi Theorem, and I was somewhat surprised to learn that Hakimi's characterization of the degree sequence in undirected graphs came over half a decade after Havel's.
Therefore, I am interested in what Hakimi's characterization provided that Havel's original characterization did not provide. The proofs that I've found of the Havel-Hakimi Theorem do not appear to make any distinction about who made which contributions.