Graphene is an outstanding electronic material, predicted to have a role in post-silicon electronics. However, owing to the absence of an electronic bandgap, graphene switching devices with high on/off ratio are still lacking. Here in the search for a comprehensive concept for wafer-scale graphene electronics, we present a monolithic transistor that uses the entire material system epitaxial graphene on silicon carbide (0001). This system consists of the graphene layer with its vanishing energy gap, the underlying semiconductor and their common interface. The graphene/semiconductor interfaces are tailor-made for ohmic as well as for Schottky contacts side-by-side on the same chip. We demonstrate normally on and normally off operation of a single transistor with on/off ratios exceeding 10(4) and no damping at megahertz frequencies. In its simplest realization, the fabrication process requires only one lithography step to build transistors, diodes, resistors and eventually integrated circuits without the need of metallic interconnects.