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Edge Disjoint Hamiltonian Cycles in Highly Connected Tournaments
International mathematics research notices
Correspondence to be sent to: firstname.lastname@example.org 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 (log k) 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.doi:10.1093/imrn/rnw009 fatcat:y77fqzls4fej3l653xl5hat3ma