Toric Ideals Generated by Circuits
Abstract
Let be the toric ideal of a homogeneous normal configuration
. We prove that
is generated by circuits if and only if each unbalanced circuit of
has a connector which is a linear combination of circuits with a square-free term. In particular, if each circuit of
with non-square-free terms is balanced, then
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.