If we have a directed graph, and the graph contains subgraphs which are out-trees. We could find the set of out-trees, such that it does not contain any out-tree that is contained by another out-tree.
EDIT: I am looking for an algorithm to calculate the set of these maximal out-trees for a given directed graph. I'm not sure if this is a problem that exists in graphs literature or not.
The number of trees may be high, but I may be able to combine trees after looking at an algorithm. I came up with an algorithm for a DAG. But I really need it for the more general case