The reconstruction conjecture and edge ideals

Given a simple graph G on n vertices, we prove that it is possible to reconstruct several algebraic properties of the edge ideal from the deck of G, that is, from the collection of subgraphs obtained by removing a vertex from G. These properties include the Krull dimension, the Hilbert function, and all the graded Betti numbers i,j where j < n. We also state many further questions that arise from our study.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Kia Dalili, Sara Faridi, Will Traves
• Keywords: Algebraic Properties, DM 2008, Edge Ideal, Simple Graph