The minimum spanning strong subdigraph problem is fixed parameter tractable Original Research Article

A digraph image is strong if it contains a directed path from image to image for every choice of vertices image in image. We consider the problem (MSSS) of finding the minimum number of arcs in a spanning strong subdigraph of a strong digraph. It is easy to see that every strong digraph image on image vertices contains a spanning strong subdigraph on at most image arcs. By reformulating the MSSS problem into the equivalent problem of finding the largest positive integer image so that image contains a spanning strong subdigraph with at most image arcs, we obtain a problem which we prove is fixed parameter tractable. Namely, we prove that there exists an image algorithm for deciding whether a given strong digraph image on image vertices contains a spanning strong subdigraph with at most image arcs.