  Carbon-substituted MgB2 single crystals, Mg(B_1-xC_x)_2 of 0.3-1.0 mm size
were grown for x=0.02-0.15 by a high-pressure technique. The doping dependence
of lattice constants studied in a range of x=0.0-0.2 shows a monotonic decrease
in a, while the c parameter remains almost invariant. Using X-ray diffraction
and Auger electron spectroscopy, the solubility limit of C in MgB2 was
estimated to be about 15(+/-)1%,which is substantially larger than that
reported for the polycrystalline samples synthesized by encapsulation
techniques. Measurements of temperature dependence of magnetization and
resistivity showed a dramatic decrease in Tc with C-substitution, followed by
complete suppression of superconductivity for x>0.125. Resistivity measurements
in magnetic fields parallel and perpendicular to the basal plane of the
crystals showed a nearly isotropic state in the heavily-doped crystals (x>0.1).
