  In a single-walled carbon nanotube, we observe the spin-1/2 Kondo effect. The
energy of spin-resolved Kondo peaks is proportional to magnetic field at high
fields, contrary to recent reports. At lower fields, the energy falls below
this linear dependence, in qualitative agreement with theoretical expectations.
For even electron occupancy, we observe a spin-1 Kondo effect due to the
degeneracy of the triplet ground states. Tuning gate voltage within the same
Coulomb diamond drives a transition to a singlet ground state. We also
independently tune the energy difference between singlet and triplet states
with a magnetic field. The Zeeman splitting thus measured confirms the value of
the g-factor measured from the spin-1/2 Kondo feature.
