### Abstract

Let G be a chordal graph and I (G) its edge ideal. Let β (I (G)) = (β_{0}, β_{1}, ..., β_{p}) denote the Betti sequence of I (G), where β_{i} stands for the ith 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 Δ of dimension p whose f-vector f (Δ) = (f_{0}, f_{1}, ..., f_{p}) coincides with β (I (G)).

Original language | English |
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Pages (from-to) | 1678-1689 |

Number of pages | 12 |

Journal | Journal of Algebra |

Volume | 323 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2010 Mar 15 |

### Keywords

- Betti sequence
- Chordal graph
- Monomial ideal
- Simplicial complex
- f-Vector

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Hibi, T., Kimura, K., & Murai, S. (2010). Betti numbers of chordal graphs and f-vectors of simplicial complexes.

*Journal of Algebra*,*323*(6), 1678-1689. https://doi.org/10.1016/j.jalgebra.2009.12.029