The reconstruction conjecture and edge ideals |
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Authors: | Kia Dalili Sara Faridi Will Traves |
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Institution: | a Department of Mathematics and Statistics, Dalhousie University, Canada B3H 3J5 b Department of Mathematics, U.S. Naval Academy, 21402, USA |
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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 βi,j where j<n. We also state many further questions that arise from our study. |
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Keywords: | 05C60 13F55 |
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