Abstract In this paper by using some tools from graph theory, mainly the theorem on ear decomposition of factor-critical graphs given by L. Lovasz 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.

中文翻译：

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边缘理想幂的不可约分解

摘要 本文利用图论中的一些工具，主要是 L. Lovasz 给出的因子临界图的耳朵分解定理和 Edmonds 和 Gallai 给出的图的规范分解，我们可以描述图的边理想。作为一个应用程序，我们将我们的结果用于不可约分量的持久性、绑定 dstab 并计算图的边理想幂的不可约分量的数量。