A simple Havel-Hakimi type algorithm to realize graphical degree sequences of directed graphs

Péter L. Erdos, István Miklós, and Zoltán Toroczkai
Electronic Journal of Combinatorics 17.1 (2010): R66.
Publication Date: 
April, 2010

One of the simplest ways to decide whether a given finite sequence of positive integers can arise as the degree sequence of a simple graph is the greedy algorithm of Havel and Hakimi. This note extends their approach to directed graphs. It also studies cases of some simple forbidden edge-sets. Finally, it proves a result which is useful to design an MCMC algorithm to find random realizations of prescribed directed degree sequences.