Irreducible Decomposition of powers of edge ideals

In this paper by using some tools from graph theory, mainly the theorem on ear decomposition of factor-critical graphs given by L. Lovász and the canonical decomposition of a graph given by Edmonds and Gallai, we can describe each irreducible component of powers of edge ideals of a graph. As an application we use our results to persistence of irreducible components, to bound dstab and to count the number of irreducible components of powers of edge ideals of a graph.