Parameterized eulerian strong component arc deletion problem on tournaments ## AbstractIn the problem \OurProb, we are given a digraph $D$ and an integer $k$, and asked whether there exists a set $A'$ of at most $k$ arcs in $D$, such that if we remove the arcs of $A'$, in the resulting digraph every strong component is Eulerian. \OurProb{} is \NPh; Cechl\'{a}rov\'{a} and Schlotter (IPEC 2010) asked whether the problem is fixed-parameter tractable when parameterized by $k$. We consider the subproblem of \OurProb{} when $D$ is a tournament. We show that this problem is fixed-parameter tractable with respect to $k$.
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