Unavoidable trees in tournaments

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An oriented tree T on n vertices is unavoidable if every tournament on n vertices contains a copy of T. In this paper we give a sufficient condition for T to be unavoidable, and use this to prove that almost all labelled oriented trees are unavoidable, verifying a conjecture of Bender and Wormald. We additionally prove that every tournament on n + o(n) vertices contains a copy of every oriented tree T on n vertices with polylogarithmic maximum degree, improving a result of Kühn, Mycroft and Osthus.


Original languageEnglish
Number of pages29
JournalRandom Structures and Algorithms
Early online date9 Feb 2018
Publication statusE-pub ahead of print - 9 Feb 2018