Edge disjoint Hamiltonian cycles in highly connected tournaments

Pokrovskiy, Alexey (2019) Edge disjoint Hamiltonian cycles in highly connected tournaments. Technical Report. Birkbeck College, University of London, London, UK.

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) ≤ O(k 2 (logk) 2 ) and conjectured that there is a constant C such that f(k) ≤ 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.

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