title: cycle 'cover' that contain an edge in a digraph
body: <p>I am wondering whether there exists a fast algorithm for the following problem. Given a digraph G, possibly with loops (that is edges that begin and end at the same vertex) and the choice of an edge e in G, what is the largest (in terms of number of vertices) subgraph of G that contains e and admits a vertex disjoint cycle cover.</p>