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

Takayuki Hibi, Kyouko Kimura, Satoshi Murai

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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)).

Original languageEnglish
Pages (from-to)1678-1689
Number of pages12
JournalJournal of Algebra
Volume323
Issue number6
DOIs
Publication statusPublished - 2010 Mar 15
Externally publishedYes

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Edge Ideals
F-vector
Projective Dimension
Chordal Graphs
Betti numbers
Simplicial Complex
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Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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

In: Journal of Algebra, Vol. 323, No. 6, 15.03.2010, p. 1678-1689.

Research output: Contribution to journalArticle

Hibi, Takayuki ; Kimura, Kyouko ; Murai, Satoshi. / Betti numbers of chordal graphs and f-vectors of simplicial complexes. In: Journal of Algebra. 2010 ; Vol. 323, No. 6. pp. 1678-1689.
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