Koszul bipartite graphs

Abstract

Let G be a bipartite graph on the vertex set {1,...,d}. LetK[t1,...,td] denote the polynomial ring indindeterminates over a fieldKandK[G] the subalgebra ofK[t1,...,td] generated by all squarefree quadratic monomialstitjsuch that {i,j} is an edge ofG. LetIGdenote the toric ideal ofK[G]. In this paper, we determine the bipartite graphsGfor whichK[G] is Koszul. © 1999 Academic Press.