Directed disjoint paths remains W[1]-hard on acyclic digraphs without large grid minors

Ken-ichi Kawarabayashi, Nicola Lorenz, Marcelo Garlet Milani +1

In the Vertex Disjoint Paths with Congestion problem, the input consists of a digraph $D$, an integer $c$ and $k$ pairs of vertices $(s_i,t_i)$, and the task is to find a set of p…