In this work, extensive characterization and complementary theoretical analysis have been carried out on Au-catalyzed InP nanowires in order to understand the planar defect formation as a function of nanowire diameter. From the detailed transmission electron microscopic measurements, the density of stacking faults and twin defects are found to monotonically decrease as the nanowire diameter is decreased to 10 nm, and the chemical analysis clearly indicates the drastic impact of In catalytic supersaturation in Au nanoparticles on the minimized planar defect formation in miniaturized nanowires. Specifically, during the chemical vapor deposition of InP nanowires, a significant amount of planar defects is created when the catalyst seed sizes are increased with the lower degree of In supersaturation as dictated by the Gibbs-Thomson effect, and an insufficient In diffusion (or Au-rich enhancement) would lead to a reduced and non-uniform In precipitation at the NW growing interface. The results presented here provide an insight into the fabrication of "bottom-up" InP NWs with minimized defect concentration which are suitable for various device applications.