Sumner's conjecture

Unsolved problem in mathematics

Does every ${\displaystyle (2n-2)}$-vertex tournament contain as a subgraph every ${\displaystyle n}$-vertex oriented tree?

More unsolved problems in mathematics

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 ${\displaystyle n}$-vertex tree is a subgraph of every ${\displaystyle (2n-2)}$-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 ${\displaystyle n}$ by Daniela Kühn, Richard Mycroft, and Deryk Osthus.