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

2009/07/28 by Takayuki Hibi, Hibi, Takayuki, Kyouko Kimura +3
Mathematics · #13F55 #13P99 #52B05 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0907.4839

openalex publication_date 2009/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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)).

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