Arithmetical rank of toric ideals associated to graphs
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Abstract:
Let $I_{G} \subset K[x_{1},\ldots ,x_{m}]$ be the toric ideal associated to a finite graph $G$. In this paper we study the binomial arithmetical rank and the $G$-homogeneous arithmetical rank of $I_G$ in 2 cases:
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$G$ is bipartite,
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$I_G$ is generated by quadratic binomials.
In both cases we prove that the binomial arithmetical rank and the $G$-homogeneous arithmetical rank coincide with the minimal number of generators of $I_G$.
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Additional Information
- Anargyros Katsabekis
- Affiliation: Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece
- Email: katsabek@aegean.gr
- Received by editor(s): December 16, 2008
- Received by editor(s) in revised form: December 16, 2009
- Published electronically: May 26, 2010
- Communicated by: Bernd Ulrich
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 3111-3123
- MSC (2010): Primary 14M25, 13F20, 05C99
- DOI: https://doi.org/10.1090/S0002-9939-2010-10335-0
- MathSciNet review: 2653936