Graphs with given valences (Q1969656)

The paper contains a short proof of the Gale-Ryser theorem (which states a necessary and sufficient condition for the existence of a \((0,1)\)-matrix with prescribed vectors of row sums and column sums). Furthermore, it is shown that the Gale-Ryser theorem is logically equivalent to the Erdős-Gallai theorem (which states a necessary and sufficient condition for the existence of a graph with prescribed vector of vertex-degrees).