  In graphene, out-of-plane (flexural) vibrations and static ripples imposed by
the substrate relax the electron spin, intrinsically protected by mirror
symmetry. We calculate the relaxation times in different scenarios, accounting
for all the possible spin-phonon couplings allowed by the hexagonal symmetry of
the lattice. Scattering by flexural phonons imposes the ultimate bound to the
spin lifetimes, in the ballpark of hundreds of nano-seconds at room
temperature. This estimate and the behavior as a function of the carrier
concentration are substantially altered by the presence of tensions or the
pinning with the substrate. Static ripples also influence the spin transport in
the diffusive regime, dominated by motional narrowing. We find that the
D'yakonov-Perel' mechanism saturates when the mean free path is comparable to
the correlation length of the heights profile. In this regime, the
spin-relaxation times are exclusively determined by the geometry of the
corrugations. Simple models for typical corrugations lead to lifetimes of the
order of tens of micro-seconds.
