Powers of the vertex cover ideals
type: Item
instance of: scholarly article
title: Powers of the vertex cover ideals
zbMATH Open document ID: 1317.13027
author: Fatemeh Mohammadi
published in: Collectanea Mathematica
publication date: 2015-01-15T00:00:00Z
full work available at URL: https://biblio.ugent.be/publication/8667481
review text: Let \(G\) be a graph with the vertex set \(V(G)=\{1,\ldots,n\}\), \(\Delta(G)\) its clique complex and \(I(G)\subseteq k[x_1,\ldots,x_n]\) its vertex cover ideal. The author shows that if \(G\) has enough free vertices (that are vertices that belongs to one clique only) then all the powers of the vertex cover ideal \(I(G)\) have linear quotients, therefore they are componentwise linear. For the class of cactus graphs, the author completely characterises those graphs which are sequentially Cohen-Macaulay. The characterization is expressed in terms of the combinatorics of the graph.
reviewed by: Anda-Georgina Olteanu
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 05E40
zbMATH DE Number: 6386915
zbMATH Keywords: Cohen-Macaulay graphs
zbMATH Keywords: componentwise linear ideals
zbMATH Keywords: edge ideals
zbMATH Keywords: vertex cover ideals of graphs
MaRDI profile type: Publication
OpenAlex ID: W2092512752
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DOI: 10.1007/S13348-013-0090-7
description: scientific article; zbMATH DE number 6386915