### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

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

**Betti numbers of chordal graphs and f-vectors of simplicial complexes.** / Hibi, Takayuki; Kimura, Kyouko; Murai, Satoshi.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 323, no. 6, pp. 1678-1689. https://doi.org/10.1016/j.jalgebra.2009.12.029

}

TY - JOUR

T1 - Betti numbers of chordal graphs and f-vectors of simplicial complexes

AU - Hibi, Takayuki

AU - Kimura, Kyouko

AU - Murai, Satoshi

PY - 2010/3/15

Y1 - 2010/3/15

N2 - Let G be a chordal graph and I (G) its edge ideal. Let β (I (G)) = (β0, β1, ..., βp) denote the Betti sequence of I (G), where βi 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) = (f0, f1, ..., fp) coincides with β (I (G)).

AB - Let G be a chordal graph and I (G) its edge ideal. Let β (I (G)) = (β0, β1, ..., βp) denote the Betti sequence of I (G), where βi 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) = (f0, f1, ..., fp) coincides with β (I (G)).

KW - Betti sequence

KW - Chordal graph

KW - f-Vector

KW - Monomial ideal

KW - Simplicial complex

UR - http://www.scopus.com/inward/record.url?scp=75249090416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=75249090416&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2009.12.029

DO - 10.1016/j.jalgebra.2009.12.029

M3 - Article

AN - SCOPUS:75249090416

VL - 323

SP - 1678

EP - 1689

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 6

ER -