Constructive extensions of two results on graphic sequences

A list of nonnegative integers is graphic if it is the list of vertex degrees of a graph. Erdős–Gallai characterized graphic lists, and Gale and Ryser, independently, provided one for a bipartite graph, given two lists of nonnegative integers. We give a constructive proof of an extension of these two results.

► We provide constructive proofs of two theorems on graphic lists.
► The first construction deals with an extension of the Erdős–Gallai theorem.
► The second construction deals with the theorem of Gale and Ryser.
► Both constructions are based on a recent constructive proof of the first result.