Integral Bases and p-Twisted Digraphs

A well-known theorem in network flow theory that for a strongly- connected digraph D = (V,A) there exists a set of directed cycles whose incidence vectors from a basis for the circulation space of D and integrally span the set of integral circulations, that is every integral circulation can be written as an integral combination of these vectors. In this paper, we extend this result to general digraphs.