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Algorithms for realizing degree sequences of directed graphs

The Havel-Hakimi algorithm for constructing realizations of degree sequences for undirected graphs has been used extensively in the literature. A result by Kleitman and Wang extends the Havel-Hakimi algorithm to degree sequences for directed graphs. In this paper we go a step further and describe a modification of Kleitman and Wang's algorithm that is a more natural extension of Havel-Hakimi's algorithm, in the sense that our extension can be made equivalent to Havel-Hakimi's algorithm when the degree sequence has equal in and out degrees and an even degree sum. We identify special degree sequences, called directed 3-cycle anchored, that are ill-defined for the algorithm and force a particular local structure on all directed graph realizations. We give structural characterizations of these realizations, as well as characterizations of the ill-defined degree sequences, leading to a well-defined algorithm.