  The dichromatic number of a digraph $D$ is the minimum number of colors
needed to color its vertices in such a way that each color class induces an
acyclic digraph. As it generalizes the notion of the chromatic number of
graphs, it has been a recent center of study. In this work we look at possible
extensions of Gy\'arf\'as-Sumner conjecture. More precisely, we propose as a
conjecture a simple characterization of finite sets $\mathcal F$ of digraphs
such that every oriented graph with sufficiently large dichromatic number must
contain a member of $\mathcal F$ as an induce subdigraph.
  Among notable results, we prove that oriented triangle-free graphs without a
directed path of length $3$ are $2$-colorable. If condition of "triangle-free"
is replaced with "$K_4$-free", then we have an upper bound of $414$. We also
show that an orientation of complete multipartite graph with no directed
triangle is 2-colorable. To prove these results we introduce the notion of
\emph{nice sets} that might be of independent interest.
