Edge disjoint Hamiltonian cycles in highly connected tournaments

Abstract

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 Kühn, Lapinskas, Osthus, and Patel who showed that $f(k)\le O(k^2(\log k{)}^2)$ and conjectured that there is a constant $C$ such that $f(k)\le C{k}^2$. We prove this conjecture.

arXiv comment27 pages, 1 figure