A proof of Sumner's universal tournament conjecture for large tournaments

Abstract

Sumner's universal tournament conjecture states that any tournament on $2n-2$ vertices contains any directed tree on $n$ vertices. In this paper we prove that this conjecture holds for all sufficiently large $n$. The proof makes extensive use of results and ideas from a recent paper by the same authors, in which an approximate version of the conjecture was proved.

arXiv comment39 pages. To appear in Proceedings of the London Mathematical Society

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