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arXiv · 0812.3097

Arithmetical rank of toric ideals associated to graphs

Anargyros Katsabekis
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Abstract

Let $I_{G} \subset K[x_{1},...,x_{m}]$ 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: $G$ is bipartite, $I_G$ is generated by quadratic binomials. In both cases we prove that the binomial arithmetical rank and the $G$-arithmetical rank coincide with the minimal number of generators of $I_G$.

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Anargyros Katsabekis. 2009-12-16. Arithmetical rank of toric ideals associated to graphs. https://arxiv.org/abs/0812.3097

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