A CLASS OF HYPERGRAPHS THAT GENERALIZES CHORDAL GRAPHS

In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given by H. T. Ha and A. Van Tuyl, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal (rigid circuit) graph. R. Froberg has showed that the chordal graphs corresponds to graph algebras, R/I(G), with linear resolutions. We extend Froberg's method and show that the hypergraph algebras of generalized chordal hypergraphs, a class of hypergraphs that includes the chordal hypergraphs, have linear resolutions. The definitions we give, yield a natural higher dimensional version of the well known flag property of simplicial complexes. We obtain what we call d-flag complexes.