## Abstract

In 1982 Thomassen asked whether there exists an integer f(k,t) such that every strongly f(k,t)-connected tournament T admits a partition of its vertex set into t vertex classes V _{1},…V _{t} such that for all i the subtournament T[V _{i}] induced on T by V _{i} is strongly k-connected. Our main result implies an affirmative answer to this question. In particular we show that f(k, t)=O(k ^{7} t ^{4}) suffices. As another application of our main result we give an affirmative answer 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-factor consisting of t vertex-disjoint cycles of prescribed lengths. We show that h(t)=O(t ^{5}) suffices.

Original language | English |
---|---|

Pages (from-to) | 451-469 |

Number of pages | 19 |

Journal | Combinatorica |

Volume | 36 |

Issue number | 4 |

Early online date | 24 Jun 2015 |

DOIs | |

Publication status | Published - Aug 2016 |

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Computational Mathematics