  We consider necessary conditions for the one-body-reduced density matrix
(1RDM) to correspond to a triplet wave-function of a two electron system. The
conditions concern the occupation numbers and are different for the high spin
projections, $S_z=\pm 1$, and the $S_z=0$ projection. Hence, they can be used
to test if an approximate 1RDM functional yields the same energies for both
projections. We employ these conditions in reduced density matrix functional
theory calculations for the triplet excitations of two-electron systems. In
addition, we propose that these conditions can be used in the calculation of
triplet states of systems with more than two electrons by restricting the
active space. We assess this procedure in calculations for a few atomic and
molecular systems. We show that the quality of the optimal 1RDMs improves by
applying the conditions in all the cases we studied.
