  A theory of spin relaxation in graphene including intrinsic, Bychkov-Rashba,
and ripple spin-orbit coupling is presented. We find from spin relaxation data
by Tombros et al. [Nature 448, 571 (2007).] that intrinsic spin-orbit coupling
dominates over other contributions with a coupling constant of 3.7 meV.
Although it is 1-3 orders of magnitude larger than those obtained from first
principles, we show that comparable values are found for other honeycomb
systems, MgB2 and LiC6; the latter is studied herein by electron spin resonance
(ESR). We predict that spin coherence is longer preserved for spins
perpendicular to the graphene plane, which is beneficial for spintronics. We
identify experimental conditions when bulk ESR is realizable on graphene.
