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

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

2010-10-21

arxiv.org/abs/1010.4430v1

Mathematics

Combinatorics

39 pages. To appear in Proceedings of the London Mathematical Society

Scientific paper

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.

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