Abstract
A theorem due to Fröberg states that a simple graph is chordal if and only if the edge ideal of its complementary graph has a linear resolution. Actually, this is a characterization of the edge ideals of 2-uniform hypergraphs which have a linear resolution. In this article, edge ideals of a special kind of d-uniform hypergraphs is investigated. It is shown that if a d-uniform hypergraph is chordal then the edge ideal of its complementary hypergraph is weakly polymatroidal. This is an improvement of a theorem due to Emtander, Mohammadi and Moradi. Also, it is proved that all powers of the edge ideal of a Ferrers hypergraph are weakly polymatroidal. Finally, we show that the edge ideals of a complete admissible uniform hypergraph ℋ and are weakly polymatroidal, where is an uniform hypergraph with the edges e c for all edges e of ℋ.
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