We show that flavor effects in leptogenesis reduce the region of the see-saw parameter space where the final predictions do not depend on the initial conditions, the strong wash-out regime. In this case the lowest bounds holding on the lightest right-handed (RH) neutrino mass and on the reheating temperature for hierarchical heavy neutrinos do not get relaxed compared to the usual ones in the one-flavor approximation, M1(Treh) � 3(1.5) × 109 GeV. Flavor effects can however relax down to these minimal values the lower bounds holding for fixed large values of the decay parameter K1. We discuss a relevant definite example showing that, when the known information on the neutrino mixing matrix is employed, the lower bounds for K1 ≫ 10 are relaxed by a factor 2-3 for light hierarchical neutrinos, without any dependence on θ13 and on possible phases. On the other hand, going beyond the limit of light hierarchical neutrinos and taking into account Majorana phases, the lower bounds can be relaxed by one order of magnitude. Therefore, Majoran
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