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- W4253901360 abstract "A conjecture of Thomassen from 1982 states that for every k there is an f(k) so that every strongly f(k)-connected tournament contains k edge-disjoint Hamilton cycles. A classical theorem of Camion, that every strongly connected tournament contains a Hamilton cycle, implies that f(1) = 1. So far, even the existence of f(2) was open. In this paper, we prove Thomassen’s conjecture by showing that f(k) = O(k 2 log2 k). This is best possible up to the logarithmic factor. As a tool, we show that every strongly 104 k log k-connected tournament is k-linked (which improves a previous exponential bound). The proof of the latter is based on a fundamental result of Ajtai, Komlós and Szemerédi on asymptotically optimal sorting networks." @default.
- W4253901360 created "2022-05-12" @default.
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- W4253901360 date "2013-01-01" @default.
- W4253901360 modified "2023-09-29" @default.
- W4253901360 title "Proof of a conjecture of Thomassen on Hamilton cycles in highly connected tournaments" @default.
- W4253901360 doi "https://doi.org/10.1007/978-88-7642-475-5_75" @default.
- W4253901360 hasPublicationYear "2013" @default.
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