Highly linked tournaments with large minimum out-degree

2018/01/25 by Girão, António, Snyder, Richard · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.08249

Abstract

We prove that there exists a function f:ℕ → ℕ 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 makes progress towards resolving a conjecture of Pokrovskiy. 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.

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