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

Erey, Nursel; Hibi, Takayuki

doi:10.1090/proc/16119

The size of Betti tables of edge ideals arising from bipartite graphs
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by Nursel Erey and Takayuki Hibi PDF

Proc. Amer. Math. Soc. 150 (2022), 5073-5083 Request permission

Abstract:

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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