Given k pairs of vertices (si, ti) (1≤i≤k) of a digraph G, how can we test whether there exist k vertex-disjoint directed paths from si to ti for 1≤i≤k? This is NP-complete in general digraphs, even for k=2 , but for k=2 there is a polynomial-time algorithm when G is a tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and Thomassen . Here we prove that for all fixed k there is a polynomial-time algorithm to solve the problem when G is semicomplete.
All Science Journal Classification (ASJC) codes
- Disjoint paths
- Dynamic programming