Rocky Mountain Journal of Mathematics
For a graph of an n-cycle Δ with Alexander dual Δ∗, we study the free resolution of a subideal G (n) of the Stanley-Reisner ideal IΔ∗. We prove that if G(n) is generated by 3 generic elements of IΔ∗, then the second syzygy module of G(n) is isomorphic to the second syzygy module of (x1,x2,... ,x n). A result of Bruns shows that there is always a 3-generated ideal with this property. We show that it can be chosen to have a particularly nice form.
Gold, Leah, "Generic Subideals of Graph Ideals and Free Resolutions" (2007). Mathematics Faculty Publications. 126.