Metal-catalyzed graphitization from vapor phase sources of carbon is now an established technique for producing few-layer graphene, a candidate material of interest for post-silicon electronics. Here we describe two alternative metal-catalyzed graphene formation processes utilizing solid phase sources of carbon. In the first, carbon is introduced as part of a cosputtered Ni-C alloy; in the second, carbon is introduced as one of the layers in an amorphous carbon (a-C)/Ni bilayer stack. We examine the quality and characteristics of the resulting graphene as a function of starting film thicknesses, Ni-C alloy composition or a-C deposition method (physical or chemical vapor deposition), and annealing conditions. We then discuss some of the competing processes playing a role in graphitic carbon formation and review recent evidence showing that the graphitic carbon in the a-C/Ni system initially forms by a metal-induced crystallization mechanism (analogous to what is seen with Al-induced crystallization of amorphous Si) rather than by the dissolution-upon-heating/precipitation-upon-cooling mechanism seen when graphene is grown by metal-catalyzed chemical vapor deposition methods.