Edge-disjoint paths in digraphs with bounded independence number

Abstract

A digraph H is infused in a digraph G if the vertices of H are mapped to vertices of G (not necessarily distinct), and the edges of H are mapped to edge-disjoint directed paths of G joining the corresponding pairs of vertices of G. The algorithmic problem of determining whether a fixed graph H can be infused in an input graph G is polynomial-time solvable for all graphs H (using paths instead of directed paths). However, the analogous problem in digraphs is NP-complete for most digraphs H. We provide a polynomial-time algorithm to solve a rooted version of the problem, for all digraphs H, in digraphs with independence number bounded by a fixed integer α. The problem that we solve is a generalization of the k edge-disjoint directed paths problem (for fixed k).