Spanning arborescences, ingraphs, and outgraphs
Kenneth A. Berman · Journal of Graph Theory · 1979
Abstract An ingraph N is a subgraph of a digraph G whose edge set consists of all the edges of G that are directed into a subset X of the vertices. Set X is the generating set of N. It is proved that G contains a unique even ingraph and this ingraph is generated by the set A of vertices that root an odd number of spanning out arborescences provided A is nonempty. If A is empty, then there exist at least two even ingraphs.