Discrete Math Seminar

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 …