# Edge-disjoint Hamilton cycles in highly strongly connected tournaments.

**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.