The Reconstruction Conjecture and Edge Ideals
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2008
- Accession Number
- ADA519092
Entities
People
- Kia Dalili
- Sara Faridi
- Will Traves