Betti numbers of toric ideals of graphs: A case study
Abstract
We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this family admits an initial ideal which has linear quotients. As a corollary, we compute the Hilbert series and h-vector for all the toric ideals of graphs in this family.
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