Threshold Digraphs
Brian Cloteaux, M. Drew LaMar, Elizabeth Moseman, James Shook
TL;DR
This paper characterizes threshold digraphs, introduces a new characterization, and provides simplified proofs of existing theorems related to degree sequences and realizations of directed graphs.
Contribution
It presents a novel characterization of threshold digraphs, simplifying proofs of known theorems and establishing equivalences among multiple characterizations.
Findings
New characterization of threshold digraphs
Simplified proof of the Fulkerson-Chen theorem
Equivalence of multiple threshold digraph characterizations
Abstract
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.
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