A many-to-many k-disjoint path cover (k-DPC for short) of a graph G joining the pairwise disjoint vertex sets S and T , each of size k, is a collection of k vertex-disjoint paths between S and T , which altogether cover every vertex of G. This is classified as paired, if each vertex of S must be joined to a specific vertex of T , or unpaired, if there is no such constraint. In this paper, we de...