On enumerating all minimal solutions of feedback problems

We present an algorithm that generates all (inclusion-wise) minimal feedback vertex sets of a directed graph G = (V, E). The feedback vertex sets of G are generated with a polynomial delay of O ( |V |(|V | + |E|) ) . We further show that the underlying technique can be tailored to generate all minimal solutions for the undirected case and the directed feedback arc set problem, both with a polynomial delay of O ( |V | |E| (|V |+ |E|) ) . Finally we prove that computing the number of minimal feedback arc sets is #P-hard.