induces a 3-cycle, then we check whether T ?N + (v) contains a cycle C. If yes, we extend (T [N + (v)], C) into a (1, 1)-outdegree-splitting by Proposition 32. If not, for every w (v), we check if T ? {u, v, w} contains a cycle C(uvw) If yes for at least one choice of {u, w}, then we extend (uvw, C(uvw)) into a (1, 1)-outdegree-splitting by Proposition 32 and we return 'no' otherwise. This is valid by Lemma 34, )-findsplit runs in O(n 2 ) time ,

-strong tournament has minimum outdegree at least f T (k 1 , k 2 ) and thus admits a (k 1 , k 2 )-outdegreesplitting . Therefore, it is natural to ask the following ,

2] proved that if T is a tournament of order 8 and xy an arc in T such that T \ xy is 2-strong, then T contains an outdegree-1-splitting (V x , V y ) ,

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