The phase diagram of the ferromagnetic Kondo model for manganites was recently investigated using computational techniques by Yunoki et al.[Phys. Rev. Lett. 80, 845 (1998)]. In dimensions 1, 2, and∞ and using classical localized spins, this study suggested a rich low-temperature phase diagram with three dominant regions:(i) a ferromagnetic phase,(ii) phase separation between hole-undoped antiferromagnetic and hole-rich ferromagnetic domains, and (iii) a phase with incommensurate spin correlations. The purpose of the present paper is twofold:(a) First, a variety of computational results is here provided to substantiate and supplement the previous results by Yunoki et al., investigating a complementary region of couplings and densities;(b) second, studies using the Lanczos algorithm and the density matrix renormalization group method applied to chains with localized spin 1/2 (with and without Coulombic repulsion for the mobile electrons) and spin 3/2 degrees of freedom are discussed. The overall conclusion is that using fully quantum mechanical localized spins in one-dimensional systems, the phase diagram of the model is similar to the result obtained using classical t 2 g spins. This result provides support of the use of classical localized spins in more complicated problems, such as in dimensions larger than 1 and/or including phononic and orbital degrees of freedom, where the use of classical spins is crucial to simplify the complexity of the problem.