Quasi-forest simplicial complexes and almost Cohen-Macaulay

2022/06/08 by Chwas Ahmed, Амир Мафи, Ahmed, Chwas +3
Computer Science · Mathematics · #13C13 #13C15 #13H10 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2206.03704

openalex publication_date 2022/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the quasi-forest simplicial complexes and we define the concept of simplicial k-cycle (denoted by S_k) and simplicial k-point (denoted by P_k). We show that a simplicial complex Δ is quasi-forest if and only if it does not have any P_k and any S_k for k≥ 3. Furthermore we characterize almost Cohen-Macaulay quasi-forest simplicial complexes. In the end we show that the cycle graph G=C_n is almost Cohen-Macaulay if and only if n=3,4,5,6,7,8,9,11.

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