Abstract: The topic, posets and graphs, recently comes about as a new branch of combinatorics. This paper is one on the topic.
Trying to solve a research problem posed by Trotter in[1]. we constructively prove the following theorem of the necessary and sufficient conditions for a digraph to be a posetable digraph.
Theorem. A digraph D is a posetable digraph if and only if D-a contains no directed path between u and v for any arc a=(u, v) of D.