  If X is a smooth projective complex threefold, the Hodge conjecture holds for
degree 4 rational Hodge classes on X. Kollar gave examples where it does not
hold for integral Hodge classes of degree 4, that is integral Hodge classes
need not be classes of algebraic 1-cycles with integral coefficients. We show
however that the Hodge conjecture holds for integral Hodge classes of degree 4
on a uniruled or a Calabi-Yau threefold.
