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A proof of Sumner’s universal tournament conjecture for large tournaments. (English) Zbl 1218.05034
In 1971, D. Sumner conjectured that if $$T$$ is any directed tree on $$n$$ vertices and $$G$$ is any tournment on $$2n- 2$$ vertices, then $$G$$ contains a copy of $$T$$. The authors prove that this conjecture holds for all sufficiently large values of $$n$$. [For the formulation of Sumner’s conjecture see http://www.math.uiuc.edu/~west/openp/univtourn.html.]

##### MSC:
 05C05 Trees 05C20 Directed graphs (digraphs), tournaments 05C35 Extremal problems in graph theory
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