# k-splittable flow problem

The maximum k-splittable s-t flow problem(MkSF) that aims to find a maximum k-splittable flow between a given source and sink node is NP-hard. We do not require the paths to be disjoint, not even different.

As a special case, just to be sure, is still computation of the k-splittable s-t flow in a directed network NP-hard if we consider only k disjoint paths?

Next, is it true if I say that for a directed network with finite number of nodes and arcs, the number of disjoint paths between two given nodes is still finite?