Arithmetical rank of toric ideals associated to graphs

Abstract

Let I G C 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: (1) G is bipartite, (2) 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 .