Sliding friction experiments on graphene grown on SiC(0001) have been performed using a combination of a microtribometer with an atomic force microscope (AFM) allowing for the investigation of atomic-scale wear. The graphene layer delaminates within 10 sliding cycles starting from substrate step edges. After run in, friction is dominated by the interaction between a changing configuration of asperities at the probe sphere and a graphitic interface layer terminating the SiC substrate. Friction varies unpredictably due to changes in the contact configuration. However, the linear relation between friction and contact area can be confirmed and a shear strength as low as a few MPa is found for the contact between ruby and the graphitic layer on SiC, which remains intact under continuous sliding.