Minimum number of arcs in $k$-critical digraphs with order at most $2k-1$

Lucas Picasarri-Arrieta, Michael Stiebitz

The dichromatic number $\vec{\chi }(D)$ of a digraph $D$ is the least integer $k$ for which $D$ has a coloring with $k$ colors such that there is no monochromatic directed cycle in $D$.…