The size of Betti tables of edge ideals arising from bipartite graphs

8 Mar 2021  ·  Nursel Erey, Takayuki Hibi ·

Let $\operatorname{pd}(I(G))$ and $\operatorname{reg}(I(G))$ respectively denote the projective dimension and the regularity of the edge ideal $I(G)$ of a graph $G$. For any positive integer $n$, we determine all pairs $(\operatorname{pd}(I(G)),\, \operatorname{reg}(I(G)))$ as $G$ ranges over all connected bipartite graphs on $n$ vertices...

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Commutative Algebra Combinatorics