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- W3158379883 abstract "Abstract Gyárfás and Sárközy conjectured that every Latin square has a “cycle‐free” partial transversal of size . We confirm this conjecture in a strong sense for almost all Latin squares, by showing that as , all but a vanishing proportion of Latin squares have a Hamilton transversal, that is, a full transversal for which any proper subset is cycle‐free. In fact, we prove a counting result that in almost all Latin squares, the number of Hamilton transversals is essentially that of Taranenko's upper bound on the number of full transversals. This result strengthens a result of Kwan (which in turn implies that almost all Latin squares also satisfy the famous Ryser–Brualdi–Stein conjecture)." @default.
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- W3158379883 date "2022-06-14" @default.
- W3158379883 modified "2023-09-26" @default.
- W3158379883 title "Hamilton transversals in random Latin squares" @default.
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- W3158379883 doi "https://doi.org/10.1002/rsa.21102" @default.
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