Saturation and associated primes of powers of edge ideals
  For the edge ideal I of an arbitrary simple graph G we describe the monomials of the saturation of a power of I in terms of (vertex) weighted graphs associated with the monomials. This description allows us to characterize the embedded associated primes of a power of I as covers of G which contain certain types of subgraphs of G. As an application, we completely classify the associated primes of the second and the third power of I in terms of G. 
Ha Thi Thu Hien, Ha Minh Lam and Ngo Viet Trung
math.AC