In theory any molecule that looks like a graphite layer should be enough. In practice there are plenty of concerns about the stability of the ones that aren't rolled into tubes (and some concern about those later ones too).
The result is, you'll see plenty of calculations telling it's possible. But it is probably not.
It definitely is with a tapered cable. The only question is if it could be done practically and if it would actually be worth the hassle. The self support length is for a cylinder of the material, with a cone there isn't a limit to the maximum self support length as the base just gets as wide as necessary to support the rest of it. But with graphene it's close enough that just a 10 to 1 difference in the cross-sectional area between the top of the cable and the bottom would be structurally sufficient. Since the area scales with the square of the radius a 10 to 1 difference is only sqrt(10) larger in diameter between the top and the bottom.
None of that answers whether the structural properties of graphene can be realized at the macroscopic level with such a massive cable. We don't know yet, because nobody has built something even close to that out of graphene.
