Sumner's conjecture

Statement

Sumner's conjecture (also called Sumner's universal tournament conjecture) is a conjecture in extremal graph theory on oriented trees in tournaments. It states that every orientation of every $n$-vertex tree is a subgraph of every $(2n-2)$-vertex tournament. David Sumner, a graph theorist at the University of South Carolina, conjectured in 1971 that tournaments are universal graphs for polytrees. The conjecture was proven for all large $n$ by Daniela Kühn, Richard Mycroft, and Deryk Osthus.