Koszul bipartite graphs
type: Item
instance of: scholarly article
title: Koszul bipartite graphs
zbMATH Open document ID: 0916.05046
author: Hidefumi Ohsugi
author: Takayuki Hibi
published in: Advances in Applied Mathematics
publication date: 1999-04-11T00:00:00Z
review text: Let \(R = K[t_1, \ldots , t_d]\) be the polynomial ring in \(d\) indeterminates over a field \(K\). If \(G\) is a bipartite graph on the vertex set \(\{ 1, \ldots , d \}\), define \(K[G]\) to be the subalgebra of \(R\) generated by all monomials \(t_i t_j\) such that \(\{ i,j \}\) is an edge of \(G\). It is shown that if every \(n\)-cycle \((n \geq 6)\) has a chord, then \(K[G]\) is Koszul.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 1247939
zbMATH Keywords: bipartite graph
zbMATH Keywords: Koszul algebra
reviewed by: Norman F. Quimpo
MaRDI profile type: Publication
full work available at URL: aama.1998.0615
OpenAlex ID: W2082136131
cites work: Q3708148
cites work: Q4245145
cites work: Toric ideals generalized by quadratic binomials
DOI: 10.1006/AAMA.1998.0615
description: scientific article; zbMATH DE number 1247939