A constructive proof of the Fulkerson–Ryser characterization of digraphic sequences

Analogous to the Erdos–Gallai inequalities that give necessary and sufficient conditions for the existence of a graph on [Formula: see text] vertices with prescribed vertex degrees, the Ryser–Fulkerson inequalities give necessary and sufficient conditions for the existence of a digraph on [Formula: see text] vertices with prescribed indegrees and outdegrees of the vertices. In this note, we give a short constructive proof of the sufficiency of the Ryser–Fulkerson inequalities.