  In the present work, we calculate the conductance through a single quantum
dot weakly coupled to metallic contacts. We use the spin-1/2 Anderson model to
describe the quantum dot, while considering a finite Coulomb repulsion. We
solve the interacting system using the non-crossing-approximation (NCA) and the
one-crossing approximation (OCA). We obtain the linear response conductance as
a function of temperature and energy position of the localized level. From the
comparison of both approximations we extract the role of the vertex
corrections, which are introduced in the OCA calculations and neglected in the
NCA scheme. As a function of the energy position, we observe that the diagrams
omitted within NCA are really important for appropriately describing transport
phenomena in Kondo systems as well as in the mixed valence regime. On the other
hand, as a function of temperature, the corrections introduced by OCA partly
recover the universal scaling properties known from numerical approaches such
as the Numerical Renormalization Group(NRG).
