Betti numbers of chordal graphs and $f$-vectors of simplicial complexes

Takayuki Hibi, Kyouko Kimura, Satoshi Murai

Let $G$ be a chordal graph and $I(G)$ its edge ideal. Let $\beta (I(G))=({\beta }_0,{\beta }_1,...,{\beta }_p)$ denote the Betti sequence of $I(G)$, where ${\beta }_i$ stands for the $i$th total Betti number…