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

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

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 $(k-1)^2$ suffices, which was improved in 2013 to $\frac{k^2}{2} - \frac{k}{2} + 1$ by Addario-Berry et al. In this talk, we give the first subquadratic bound for Burr's …