A hypergraph pair is a pair (G,H) where G and H are hypergraphs on the same set of vertices. We extend the definitions of hypertree-width [7] and generalised hypertree-width [8] from hypergraphs to hypergraph pairs. We show that for constant k the problem of deciding whether a hypergraph pair has generalised hypertree-width ≤ k, is equivalent to the Hypergraph Sandwich Problem (HSP) [13]. It was recently proved in [9] that the HSP is NP-complete. For constant k there is a polynomial time… CONTINUE READING