Koszul Bipartite Graphs

LetGbe a bipartite graph on the vertex set {1,?,d}. LetKt1,?,td] denote the polynomial ring indindeterminates over a fieldKandKG] the subalgebra ofKt1,?,td] generated by all squarefree quadratic monomialstitjsuch that {i,j} is an edge ofG. LetIGdenote the toric ideal ofKG]. In this paper, we determine the bipartite graphsGfor whichKG] is Koszul.