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arXiv · 1807.02154

Betti numbers of toric ideals of graphs: A case study

Federico Galetto·Johannes Hofscheier·Graham Keiper·Craig Kohne·Miguel Eduardo Uribe Paczka·Adam Van Tuyl
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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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Federico Galetto, Johannes Hofscheier, Graham Keiper, Craig Kohne, Miguel Eduardo Uribe Paczka, Adam Van Tuyl. 2018-07-05. Betti numbers of toric ideals of graphs: A case study. https://doi.org/10.1142/s0219498819502268

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