  A digraph whose degree sequence has a unique vertex labeled realization is
called threshold. In this paper we present several characterizations of
threshold digraphs and their degree sequences, and show these characterizations
to be equivalent. One of the characterizations is new, and allows for a shorter
proof of the equivalence of the two known characterizations as well as proving
the final characterization which appears without proof in the literature. Using
this result, we obtain a new, short proof of the Fulkerson-Chen theorem on
degree sequences of general digraphs.
