We propose a new consistency condition for the compatibility of a gravitational effective field theory in AdS with a dual holographic description in terms of a family of large-N CFTs. Using large-N factorization of correlation functions combined with a properly defined notion of single- and multi-particle operators, we argue that the cubic scalar bulk couplings for fields dual to operators with extremal arrangements of the conformal dimensions, i.e. Δi=Δj+Δk, should vanish. Finally, we apply this criterion to the 4d  effective supergravity theory describing the DGKT AdS4 vacua in type IIA string theory.