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Our main result implies an affirmative answer to this question. In particular we show that f(k,t) = O(k^7 t^4) suffices. As another application of our main result we give an affirmative answer to a question of Song as to whether, for any integer t, there exists an integer h(t) such that every strongly h(t)-connected tou"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.7677","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-29T23:57:24Z","cross_cats_sorted":[],"title_canon_sha256":"1775f81edc1a803ef5945accf59b40dd6b41891f20037fabd79f3a0336048d2e","abstract_canon_sha256":"1838d3d8ecc6bfb454f2a8901c6a57855b5e7bb35713114789405d8923aa0a18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:46.779499Z","signature_b64":"w+notYz/7a8P0Np/T4gDqQlUCfhL2UXSezt83ZEowkLj9TBY7ERnyiLAbnc3EGt6ym2q5MJ/KVJvkv1x7XxdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"164f2f188ffbd9d341916affd54e55482921910674aa9480c075ab64f5871a78","last_reissued_at":"2026-05-18T01:27:46.778963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:46.778963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof of a tournament partition conjecture and an application to 1-factors with prescribed cycle lengths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniela K\\\"uhn, Deryk Osthus, Timothy Townsend","submitted_at":"2013-09-29T23:57:24Z","abstract_excerpt":"In 1982 Thomassen asked whether there exists an integer f(k,t) such that every strongly f(k,t)-connected tournament T admits a partition of its vertex set into t vertex classes V_1,...,V_t such that for all i the subtournament T[V_i] induced on T by V_i is strongly k-connected. 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