A Simple Havel–Hakimi Type Algorithm to Realize Graphical Degree Sequences of Directed Graphs

Péter L. Erdős, István Miklós, Zoltán Toroczkai


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.

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