Highly linked tournaments with large minimum out-degree

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Abstract

We prove that there exists a function f:NN such that for any positive integer k, if T is a strongly 4k-connected tournament with minimum out-degree at least f(k), then T is k-linked. This resolves a conjecture of Pokrovskiy up to a factor of 2 of the required connectivity. Along the way, we show that a tournament with sufficiently large minimum out-degree contains a subdivision of a complete directed graph. This result may be of independent interest.

Keywords

Tournaments
Connectivity of tournaments
Linkedness
Subdivisions in tournaments

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