We study the binding of molecular oxygen to a graphene sheet and to a (8,0) single walled carbon nanotube, by means of spin-unrestricted density-functional calculations. We find that triplet oxygen retains its spin-polarized state when interacting with graphene or the nanotube. This leads to the formation of a weak bond with essentially no charge transfer between the molecule and the sheet or tube, as one would expect for a physisorptive bond. This result is independent on the approximation used for the exchange-correlation functional. The binding strength, however, depends strongly on the functional, reflecting the inability of current approximation functionals to deal correctly with dispersion forces. Gradient-corrected functionals yield very weak binding at distances around 4 Angstrom, whereas local density functional results yield substantially stronger binding for both graphene and the nanotube at distances of less than 3 Angstrom. The picture of oxygen physisorption is not substantially altered by the presence of topological defects such as 5-7 Stone-Wales pairs. (C) 2003 American Institute of Physics.