Structural and transport properties of individual micron-sized graphitic disks with less than one hundred graphene layers are measured. Mesoscopic devices of any arbitrary geometry can be fabricated at the center of such disks by focussed ion beam lithography, with the rest of the disk serving as low-resistance contacts. Our approach is exemplified by the fabrication and characterization of 30 to 60 nm wide point-contact devices. A size effect is revealed by the suppression of the magnetoresistance in constrictions narrower than the smallest attained cyclotron orbit for fields up to 10 T.

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