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

Takayuki Hibi; Kyouko Kimura; Satoshi Murai

doi:10.1016/j.jalgebra.2009.12.029

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

Takayuki Hibi, Kyouko Kimura^*, Satoshi Murai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let G be a chordal graph and I (G) its edge ideal. Let β (I (G)) = (β₀, β₁, ..., 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) = (f₀, f₁, ..., 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	https://doi.org/10.1016/j.jalgebra.2009.12.029
Publication status	Published - 2010 Mar 15
Externally published	Yes

Keywords

Betti sequence
Chordal graph
Monomial ideal
Simplicial complex
f-Vector

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2009.12.029

Cite this

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title = "Betti numbers of chordal graphs and f-vectors of simplicial complexes",

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)).",

keywords = "Betti sequence, Chordal graph, Monomial ideal, Simplicial complex, f-Vector",

author = "Takayuki Hibi and Kyouko Kimura and Satoshi Murai",

note = "Funding Information: E-mail addresses: hibi@math.sci.osaka-u.ac.jp (T. Hibi), kimura@math.sci.osaka-u.ac.jp (K. Kimura), murai@yamaguchi-u.ac.jp (S. Murai). 1 The author is supported by JSPS Research Fellowships for Young Scientists.",

year = "2010",

month = mar,

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doi = "10.1016/j.jalgebra.2009.12.029",

language = "English",

volume = "323",

pages = "1678--1689",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

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TY - JOUR

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

AU - Hibi, Takayuki

AU - Kimura, Kyouko

AU - Murai, Satoshi

N1 - Funding Information: E-mail addresses: hibi@math.sci.osaka-u.ac.jp (T. Hibi), kimura@math.sci.osaka-u.ac.jp (K. Kimura), murai@yamaguchi-u.ac.jp (S. Murai). 1 The author is supported by JSPS Research Fellowships for Young Scientists.

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 - Monomial ideal

KW - Simplicial complex

KW - f-Vector

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DO - 10.1016/j.jalgebra.2009.12.029

M3 - Article

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SN - 0021-8693

VL - 323

SP - 1678

EP - 1689

JO - Journal of Algebra

JF - Journal of Algebra

IS - 6

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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