  We show that a necessary condition to have a positive Landau-gauge ghost
propagator in d=2 Yang-Mills theories is a vanishing zero-momentum gluon
propagator. Our proof is based on a careful scrutinizing of the ghost
Dyson-Schwinger equation. Said otherwise, the Gribov no-pole condition forbids
the occurrence of the "decoupling/massive" gluon propagator solution in d=2, in
sharp contrast with d=3 and 4, but consistent with state-of-the-art lattice
data.
