Graph connectivity and binomial edge ideals
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- by Arindam Banerjee and Luis Núñez-Betancourt PDF
- Proc. Amer. Math. Soc. 145 (2017), 487-499 Request permission
Abstract:
We relate homological properties of a binomial edge ideal $\mathcal {J}_G$ to invariants that measure the connectivity of a simple graph $G$. Specifically, we show if $R/\mathcal {J}_G$ is a Cohen-Macaulay ring, then graph toughness of $G$ is exactly $\frac {1}{2}$. We also give an inequality between the depth of $R/\mathcal {J}_G$ and the vertex-connectivity of $G$. In addition, we study the Hilbert-Samuel multiplicity and the Hilbert-Kunz multiplicity of $R/\mathcal {J}_G$.References
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Additional Information
- Arindam Banerjee
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-2067
- MR Author ID: 1095868
- Email: banerj19@purdue.edu
- Luis Núñez-Betancourt
- Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22904-4135 – and – Centro de Investigación en Matemáticas, Guanajuato, Gto., México
- MR Author ID: 949465
- Email: luisnub@cimat.mx
- Received by editor(s): January 23, 2016
- Received by editor(s) in revised form: April 4, 2016
- Published electronically: August 18, 2016
- Additional Notes: The second author gratefully acknowledges the support of the National Science Foundation for support through Grant DMS-1502282
- Communicated by: Irena Peeva
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 487-499
- MSC (2010): Primary 13C14, 05C40, 05E40
- DOI: https://doi.org/10.1090/proc/13241
- MathSciNet review: 3577855