Oriented trees in $O(k\sqrt{k})$-chromatic digraphs, a subquadratic bound for Burr's conjecture

Stéphane Bessy, Daniel Gonçalves, Amadeus Reinald

In 1980, Burr conjectured that every directed graph with chromatic number $2k-2$ contains any oriented tree of order $k$ as a subdigraph. Burr showed that chromatic number $(k-1)^2…