Is the valency of carbon satisfied in graphite?
In the hexagonal graphite structure the carbon atoms are $\ce{sp^2}$ hybridized, just like in benzene.  In graphite, this p-orbital is used for bonding just as it is in benzene, resulting in an extended pi system in the graphite structure.  Graphite is really just a large number of benzene rings annelated together to form a continuous, ring structure.  Just as carbon satisfies its valence requirement of 4 in benzene (3 sigma bonds and 1 pi bond), carbon's valency requirements are satisfied the same way in graphite.