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Trees in tournaments. (English) Zbl 1048.05040
Summary: In 1971, Sumner conjectured that any tournament of order \(2(n-1)\) contains any oriented tree of order \(n\). Since then several bounds have been established that get closer and closer to the suggested bound \(2(n-1)\). In this paper we prove that any tournament of order \(3(n-1)\) contains any oriented tree of order \(n\).

MSC:
05C20 Directed graphs (digraphs), tournaments
05C05 Trees
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