Steiner connectivity problems in hypergraphs

We say that a tree T is an S-Steiner if S⊆V(T) and hypergraph hypertree it can be trimmed to tree. prove NP-complete decide, given H some S⊆V(H), whether there subhypergraph of which hypertree. As corollaries, we give two negative results for Steiner orientation problems in hypergraphs. Firstly, show H, r∈V(H) this has every vertex S reachable from r. Secondly, any vertices are mutually each other. This answers longstanding open question the Egerváry Research group. further decide well-balanced orientation. On positive side, problem finding first solved polynomial time number terminals |S| fixed.