Toric ideals generated by circuits
  Let I be the toric ideal of a homogeneous normal configuration. We prove that I is generated by circuits if and only if each unbalanced circuit of I has a "connector" which is a linear combination of circuits with a square-free term. In particular if each circuit of I with non-square-free terms is balanced, then I is generated by circuits. As a consequence we prove that the toric ideal of a normal edge subring of a multigraph is generated by circuits with a square-free term. 
Jose Martinez-Bernal and Rafael H. Villarreal