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Threshold Digraphs



Brian D. Cloteaux, Michael D. LaMar, Elizabeth R. Moseman, James Shook


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.
Siam Journal on Discrete Mathematics


threshold, digraph, degree sequence, graphicality testing


Cloteaux, B. , LaMar, M. , Moseman, E. and Shook, J. (2012), Threshold Digraphs, Siam Journal on Discrete Mathematics, [online], (Accessed July 24, 2024)


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Created December 5, 2012, Updated February 19, 2017