Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers

Abstract We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The theme of this paper is to understand how the combinatorial structure of a hypergraph ℋ appears within the resolution of its edge ideal ℐ(ℋ). We discuss when recursive formulas to compute the graded Betti numbers of ℐ(ℋ) in terms of its sub-hypergraphs can be obtained; these …