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

Abstract

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.

11 pages, 1 figure submitted to "The Electronic Journal of Combinatorics"

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