  We present a comparative study of the density dependence of the conductivity
of graphene sheets calculated in the tight-binding (TB) Landauer approach and
on the basis of the Boltzmann theory. The TB calculations are found to give the
same density dependence of the conductivity, $\sigma \sim n$, for short-range
and long-range Gaussian scatterers. In the case of short-range scattering the
TB calculations are in agreement with the predictions of the Boltzmann theory
going beyond the Born approximation, but in qualitative and quantitative
disagreement with the standard Boltzmann approach within the Born
approximation, predicting $\sigma= $ const. Even for the long-range Gaussian
potential in a parameter range corresponding to realistic systems the standard
Boltzmann predictions are in quantitative and qualitative disagreement with the
TB results. This questions the applicability of the standard Boltzmann approach
within the Born approximation, commonly used for the interpretation of the
results of experimental studies of the transport in graphene.
