A digraph whose degree sequences have a unique vertex labeled realization is called threshold. In this paper we present several characterizations of threshold digraphs and show them 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.
Citation: Siam Journal on Discrete Mathematics
Pub Type: Journals
threshold, digraph, degree sequence, graphicality testing