  In a recent preprint Kong et al, arXiv:0902.0642v1 (2009) claimed to
calculate the lattice thermal conductivity of single and bi-layer graphene
'from first principles'. The main findings were that the Umklapp-limited
thermal conductivity is only slightly higher than that of high-quality bulk
graphite along the basal plane, and that it does not strongly depend on the
number of atomic layers. Here we explain that the calculation of Kong et al
used a truncation procedure with a 'hidden' parameter, a cut-off frequency for
the long-wavelength acoustic phonons, which essentially determined the final
result. Unlike in bulk graphite, there is no physical justification for
introducing the cut-off frequency for the long wavelength phonons in graphene.
It leads to substantial underestimation of graphene's lattice thermal
conductivity and a wrong conclusion about the dependence on the number of
atomic layers. We outline the proper way for calculating the lattice thermal
conductivity of graphene, which requires an introduction of other scattering
mechanisms to avoid a logarithmic divergence of the thermal conductivity
integral.
