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Tree-related Widths of Graphs and Hypergraphs

Summary: Tree-related Widths of Graphs and
Isolde Adler
Mathematisches Institut,
Eckerstr. 1,
D-79102 Freiburg
23rd May 2007
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


Source: Adler, Isolde - Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt am Main


Collections: Computer Technologies and Information Sciences