  We observe that nonzero Gromov-Witten invariants with marked point
constraints in a closed symplectic manifold imply restrictions on the homology
classes that can be represented by contact hypersurfaces. As a special case,
contact hypersurfaces must always separate if the symplectic manifold is
uniruled. This removes a superfluous assumption in a result of G. Lu, thus
implying that all contact manifolds that embed as contact type hypersurfaces
into uniruled symplectic manifolds satisfy the Weinstein conjecture. We prove
the main result using the Cieliebak-Mohnke approach to defining Gromov-Witten
invariants via Donaldson hypersurfaces, thus no semipositivity or virtual
moduli cycles are required.
