A short constructive proof of the Erdos-Gallai characterization of graphic lists

Erdős and Gallai proved that a nonincreasing list (d1, . . . , dn) of nonnegative integers is the list of degrees of a graph (with no loops or multi-edges) if and only if the sum is even and the list satisfies ∑k i=1 di ≤ k(k−1)+ ∑n i=k+1 min{k, di} for 1 ≤ k ≤ n. We give a short constructive proof of the characterization. AMS Subject classification: 05C07