  We show that the Koszul homology algebra of a quotient by the edge ideal of a
forest is generated by the lowest linear strand. This provides a large class of
Koszul algebras whose Koszul homology algebras satisfy this property. We obtain
this result by constructing the minimal graded free resolution of a quotient by
such an edge ideal via the so called iterated mapping cone construction and
using the explicit bases of Koszul homology given by Herzog and Maleki. Using
these methods we also recover a result of Roth and Van Tuyl on the graded Betti
numbers of quotients of edge ideals of trees.
