Parameterized Eulerian Strong Component Arc Deletion Problem on Tournaments

In the problemMin-DESC, we are given a digraphD and an integer k, and asked whether there exists a set A of at most k arcs inD, such that if we remove the arcs of A, in the resulting digraph every strong component is Eulerian. Min-DESC is NP-hard; Cechlárová and Schlotter (IPEC 2010) asked whether the problem is fixed-parameter tractable when parameterized by k. We consider the subproblem of Min-DESC whenD is a tournament. We show that this problem is fixed-parameter tractable with respect to k.