Extremal Betti numbers of edge ideals

Takayuki Hibi, Kyouko Kimura, Kazunori Matsuda

Given integers $r$ and $b$ with $1\le b\le r$, a finite simple connected graph $G$ for which $\mathrm{reg}(S/I(G))=r$ and the number of extremal Betti numbers of $S/I(G)$ is equ…