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In 1982 Thomassen asked whether there exists an integer f(k,t) such thatevery strongly f(k,t)-connected tournament T admits a partition of its vertexset into t vertex classes V_1,...,V_t such that for all i the subtournamentT[V_i] induced on T by V_i is strongly k-connected. Our main result implies anaffirmative answer to this question. In particular we show that f(k,t) = O(k^7t^4) suffices. As another application of our main result we give an affirmativeanswer to a question of Song as to whether, for any integer t, there exists aninteger h(t) such that every strongly h(t)-connected tournament has a 1-factorconsisting of t vertex-disjoint cycles of prescribed lengths. We show that h(t)= O(t^5) suffices.

Proof of a tournament partition conjecture and an application to 1-factors with prescribed cycle lengths