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arXiv · 1010.4429

An approximate version of Sumner's universal tournament conjecture

Daniela Kühn·Richard Mycroft·Deryk Osthus
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Abstract

Sumner's universal tournament conjecture states that any tournament on $2n-2$ vertices contains a copy of any directed tree on $n$ vertices. We prove an asymptotic version of this conjecture, namely that any tournament on $(2+o(1))n$ vertices contains a copy of any directed tree on $n$ vertices. In addition, we prove an asymptotically best possible result for trees of bounded degree, namely that for any fixed $\Delta$, any tournament on $(1+o(1))n$ vertices contains a copy of any directed tree on $n$ vertices with maximum degree at most $\Delta$.

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Daniela Kühn, Richard Mycroft, Deryk Osthus. 2010-10-21. An approximate version of Sumner's universal tournament conjecture. https://doi.org/10.1016/j.jctb.2010.12.006

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