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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2008
Accession Number
ADA519092

Entities

People

  • Kia Dalili
  • Sara Faridi
  • Will Traves

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Coverings
  • Decomposition
  • Electronic Mail
  • Graph Theory
  • Inclusions
  • Information Operations
  • Mathematics
  • Polynomials
  • Sequences
  • Statistics
  • United States
  • United States Naval Academy
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.