Existence of circuit passing through each vertex in a directed graph Are there necessary and sufficient conditions for the existence of a circuit, or a disjoint set of circuits, that passes through each vertex once in a directed graph?

A collection of disjoint cycles that cover all vertices of an (undirected) graph is known as a 2-factor. This paper references some criterion of Tutte for the existence of these, which, paraphrasing the authors, in some sense completely solves the problem. It's Theorem 1 on page 2, which points to "The factors of graphs" by Tutte (1952).
