Conjecture For every , there is an integer so that every strongly -connected tournament has edge-disjoint Hamilton cycles.
Kelly made the following conjecture which replaces the assumption of high connectivity by regularity.
Conjecture Every regular tournament of order can be decomposed into Hamilton directed cycles.
Kelly's conjecture has been proved for tournaments of sufficiently large order by Kühn and Osthus [KO].
Bibliography
[KO] Daniela Kühn and Deryk Osthus, Hamilton decompositions of regular expanders: a proof of Kelly's conjecture for large tournaments, Advances in Mathematics 237 (2013), 62-146.
*[T] C. Thomassen, Edge-disjoint Hamiltonian paths and cycles in tournaments, Proc. London Math. Soc. 45 (1982), 151-168.
* indicates original appearance(s) of problem.