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arXiv · 1605.06980

Bounds on the regularity of toric ideals of graphs

Jennifer Biermann·Augustine O'Keefe·Adam Van Tuyl
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Abstract

Let $G$ be a finite simple graph. We give a lower bound for the Castelnuovo-Mumford regularity of the toric ideal $I_G$ associated to $G$ in terms of the sizes and number of induced complete bipartite graphs in $G$. When $G$ is a chordal bipartite graph, we find an upper bound for the regularity of $I_G$ in terms of the size of the bipartition of $G$. We also give a new proof for the graded Betti numbers of the toric ideal associated to the complete bipartite graph $K_{2,n}$.

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Jennifer Biermann, Augustine O'Keefe, Adam Van Tuyl. 2016-05-23. Bounds on the regularity of toric ideals of graphs. https://arxiv.org/abs/1605.06980

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