Directed 3-cycle anchored digraphs and their application in the uniform sampling of realizations from a fixed degree sequence

In this paper, we give structural and degree sequence characterizations for a new class of digraphs called directed 3-cycle anchored. A digraph in this class has the property that, for every realization of its degree sequence, there is a directed 3-cycle through each vertex of a labeled vertex set. We end by illustrating their use in the uniform sampling of simple directed graph realizations from a fixed degree sequence.