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 (∣T∣−2∣V∖T∣)⋅33∣V∖T∣ 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 to the case ∣T∣=2. We apply our enumeration algorithm
to solve the {\sc 2-Disjoint Connected Subgraphs} problem in time
O∗(1.7804n), improving on the recent O∗(1.933n) algorithm of Cygan et
al. 2012 LATIN paper.Comment: 13 pages, 1 figur