Powers of edge ideals

Abstract

We compute the Betti numbers for all the powers of initial and final lexsegment edge ideals. For the powers of the edge ideal of an anti–d−path, we prove that they have linear quotients and we characterize the normally torsion–free ideals. We determine a class of non–squarefree ideals, arising from some particular graphs, which are normally torsion–free.

Keywords

• Betti number
• Associated prime ideal
• Edge ideal
• Normally torsion-free