Arithmetical rank of toric ideals associated to graphs

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 $I_G$.

arXiv comment13 pages

Cited by in corpus (1)

• Minimal generators of toric ideals of graphs