an:07004297
Zbl 1405.05097
Pokrovskiy, Alexey
Edge disjoint Hamiltonian cycles in highly connected tournaments
EN
Int. Math. Res. Not. 2017, No. 2, 429-467 (2017).
00426601
2017
j
05C45
Summary: \textit{C. Thomassen} [Proc. Lond. Math. Soc. (3) 45, 151--168 (1982; Zbl 0486.05049)] 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 \textit{D. K??hn} et al. [Proc. Lond. Math. Soc. (3) 109, No. 3, 733--762 (2014; Zbl 1302.05069)] 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. As a second application of our methods, we answer a question of Thomassen about spanning linkages in highly connected tournaments.
Zbl 1302.05069; Zbl 0486.05049