  We investigate the Cooper-pair propagation and the proximity effect in
graphene under conditions in which the distance L between superconducting
electrodes is much larger than the width W of the contacts. In the case of
undoped graphene, supercurrents may exist with a spatial decay proportional to
W^2/L^3. This changes upon doping into a 1/L^2 behavior, opening the
possibility to observe a supercurrent over length scales above 1 micron at
suitable doping levels. We also show that there is in general a crossover
temperature T ~ v_F/k_B L that marks the onset of the strong decay of the
supercurrent, and that corresponds to the scale below which the Cooper pairs
are not disrupted by thermal effects during their propagation.
