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The Reconstruction Conjecture and Edge Ideals

Janani, Negar | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 46603 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Pournaki, Mohammad Reza
  7. Abstract:
  8. 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. We also state many further questions that arise from our study
  9. Keywords:
  10. Reconstruction Conjecture ; Edge Ideal ; Hilbert Function ; Graded Betti Numbers

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