  The SU(2) Yang-Mills gluon and ghost Green-functions are studied in Landau
gauge by means of lattice gauge simulations. A focal point is their low energy
behavior since in particular the Kugo-Ojima confinement criterion relates a
diverging ghost form factor at vanishing momentum transfer to the confining
capabilities of the theory. This divergence is verified by numerical
simulations. Removing the confining vortices from the lattice ensembles
converts SU(2) Yang-Mills theory in a non-confining theory. It is shown that in
this modified theory the divergence of the ghost propagator disappears.
