TL;DR
This paper extends the concept of split graphs to directed graphs, providing degree sequence characterizations and conditions for identifying split digraphs based on their degree sequences.
Contribution
It introduces the first degree sequence characterization of split digraphs, extending the concept of splittance and linking it to Fulkerson inequalities.
Findings
Split digraphs can be identified from their degree sequences.
A new degree sequence characterization extends splittance to directed graphs.
Split digraphs satisfy Fulkerson inequalities with equality.
Abstract
We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to directed graphs, while the second characterization says a digraph is split if and only if its degree sequence satisfies one of the Fulkerson inequalities (which determine when an integer-pair sequence is digraphic) with equality.
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