A synthesis method of strictly monolayer and fully homogeneous graphene across tens of centimeter squares, by chemical vapour deposition onto standard copper foils, is presented. The growth technique involves cyclic injection of a carbon precursor separated by idle times with constant hydrogen exposure. The formation of spurious multilayer patches, which accompanies the standard growth techniques based on continuous exposure to methane, is inhibited here, in a broad range of pressure and gas composition, including in two pressure regimes which are known to yield distinctive grain morphologies (dendritic versus hexagonal). Raman spectra confirm the absence of defects within the graphene films. A mechanism for growth/suppression of the multilayer patches based on the carbon storage at defective regions is proposed. The importance of multilayer suppression is highlighted in a comparative study showing the detrimental effect of patches on the performances of graphene transistors and on the optical transparency of stacked layers. The full-layer graphene sheets are superiorly homogeneous in terms of their optical and electronic properties, and are thus suited for applications for high-density integration as well as transparent electrodes with spatially continuous optical absorbance. Graphene transistors fabricated by the pulsed CVD method exhibit room-temperature mobilities with a mean value of 5000 cm2 V−1 s−1.