Spin transport in graphene carries the potential of a long spin diffusion length at room temperature. However, extrinsic relaxation processes limit the current experimental values to 1-2 um. We present Hanle spin precession measurements in gated lateral spin valve devices in the low to high (up to 10^13 cm^-2) carrier density range of graphene. A linear scaling between the spin diffusion length and the diffusion coefficient is observed. We measure nearly identical spin- and charge diffusion

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... ficients indicating that electron-electron interactions are relatively weak and transport is limited by impurity potential scattering. When extrapolated to the maximum carrier mobilities of 2x10^5 cm^2/Vs, our results predict that a considerable increase in the spin diffusion length should be possible.