%0 Journal Article
%T Betti numbers of chordal graphs and $f$-vectors of simplicial complexes
%A Takayuki Hibi
%A Kyouko Kimura
%A Satoshi Murai
%J Mathematics
%D 2009
%I arXiv
%X 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 of $I(G)$ and where $p$ is the projective dimension of $I(G)$. It will be shown that there exists a simplicial complex $\Delta$ of dimension $p$ whose $f$-vector $f (\Delta) = (f_0, f_1, ..., f_p)$ coincides with $\beta (I(G))$.
%U http://arxiv.org/abs/0907.4839v1