Tree-Related Widths of Graphs and Hypergraphs

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 algorithm that decides whether a given hypergraph pair has hypertree-width k. (For hypertree-width of hypergraphs, this was shown in [7].) It follows that the HSP is solvable in polynomial time for of inputs (G, H) satisfying: ghw(G, H) 1 if, and only

• Type: Journal
• Year: 2008
• Where: SIAMDM
• Authors: Isolde Adler
• Keywords: Generalised, Hypergraph Pair, Hypergraph Sandwich Problem, SIAMDM 2008