The size of the Betti table of Binomial Edge Ideals

Abstract

Let $G$ be a finite simple graph on $n$ non-isolated vertices, and let $J_G$ be its binomial edge ideal. We determine almost all pairs $(\text{projdim}(J_G),\text{reg}(J_G))$, where $G$ ranges over all finite simple graphs on $n$ non-isolated vertices, for any $n$.

This is the final version of the paper, accepted for publication in Journal of Algebra and its Applications, https://doi.org/10.1142/S0218196724500589