Given a graph G = (V,E) and a set of terminal vertices T we say that a superset S of T is T -connecting if S induces a connected graph, and S is minimal if no strict subset of S is T -connecting. In this paper we prove that there are at most (|V \T | |T |−2 ) · 3 |V \T | 3 minimal T -connecting sets when |T | ≤ n/3 and that these can be enumerated within a polynomial factor of this bound. This generalizes the algorithm for enumerating all induced paths between a pair of vertices, corresponding… CONTINUE READING