The algorithmic use of hypertree structure and maximum neighbourhood orderings Original Research Article

The use of (generalized) tree structure in graphs is one of the main topics in the field of efficient graph algorithms. The well-known partial k-tree (resp. treewidth) approach belongs to this kind of research and bases on a tree structure of constant-size bounded maximal cliques. Without size bound on the cliques this tree structure of maximal cliques characterizes chordal graphs which are known to be important also in connection with relational database schemes where hypergraphs with tree structure (acyclic hypergraphs) and their elimination orderings (perfect elimination orderings for chordal graphs, Graham-reduction for acyclic hypergraphs) are studied.