On \(m\)-closed graphs
type: Item
instance of: scholarly article
title: On \(m\)-closed graphs
zbMATH Open document ID: 1302.05163
author: Leila Sharifan
author: Masoumeh Javanbakht
published in: The Electronic Journal of Combinatorics
publication date: 2014-11-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1708.08864
full work available at URL: v21i4p26
review text: Summary: A graph is closed when its vertices have a labeling by \([n]\) such~that the binomial edge ideal \(J_G\) has a quadratic Gröbner~basis~with respect to the lexicographic order induced by \(x_1> \ldots> x_n > y_1> \ldots > y_n\). In this paper, we generalize this notion~and study the so called \(m\)-closed graphs. We find equivalent condition to \(3\)-closed property of an arbitrary tree \(T\). Using it, we classify a class of \(3\)-closed trees. The primary~decomposition of this class of graphs is also studied.
Mathematics Subject Classification ID: 05C78
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 05E40
zbMATH DE Number: 6369272
zbMATH Keywords: \(m\)-closed graph
zbMATH Keywords: binomial edge ideal
zbMATH Keywords: reduced Gröbner basis
zbMATH Keywords: admissible path
MaRDI profile type: Publication
arXiv ID: 1708.08864
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description: scientific article; zbMATH DE number 6369272