 
Summary: Treerelated Widths of Graphs and
Hypergraphs
Isolde Adler
Mathematisches Institut,
Eckerstr. 1,
D79102 Freiburg
isolde.adler@math.unifreiburg.de
23rd May 2007
Abstract
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 hypertreewidth [7]
and generalised hypertreewidth [8] from hypergraphs to hypergraph pairs.
We show that for constant k the problem of deciding whether a hypergraph
pair has generalised hypertreewidth k, is equivalent to the Hypergraph
Sandwich Problem (HSP) [13]. It was recently proved in [9] that the HSP
is NPcomplete.
For constant k there is a polynomial time algorithm that decides whether
a given hypergraph pair has hypertreewidth k. (For hypertreewidth 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
