Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals

There is a natural one-to-one correspondence between squarefree monomial ideals and finite simple hypergraphs via the cover ideal construction. Let H be a finite simple hypergraph, and let J=J(H) be its cover ideal in a polynomial ring R. We give an explicit description of all associated primes of R/Js, for any power Js of J, in terms of the coloring properties of hypergraphs arising from H. We also give an algebraic method for determining the …