Edge disjoint Hamiltonian cycles in highly connected tournaments

@article{Pokrovskiy2014EdgeDH,
  title={Edge disjoint Hamiltonian cycles in highly connected tournaments},
  author={A. Pokrovskiy},
  journal={arXiv: Combinatorics},
  year={2014}
}
Thomassen conjectured that there is a function $f(k)$ such that every strongly $f(k)$-connected tournament contains $k$ edge-disjoint Hamiltonian cycles. This conjecture was recently proved by Kuhn, Lapinskas, Osthus, and Patel who showed that $f(k)\leq O(k^2(\log k)^2)$ and conjectured that there is a constant $C$ such that $f(k)\leq Ck^2$. We prove this conjecture. 

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