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 n vertices with prescribed vertex degrees, the Ryser–Fulkerson inequalities give necessary and sufficient conditions for the existence of a digraph on n 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. [ABSTRACT FROM AUTHOR]