Jungles, bundles, and fixed parameter tractability
  We give a fixed-parameter tractable (FPT) approximation algorithm computing the path-width of a tournament, and more generally, of a semi-complete digraph. Based on this result, we prove that topological containment and rooted immersion problems are FPT on semi-complete digraphs. 
Fedor V. Fomin and Micha{\l} Pilipczuk
cs.DS math.CO