We characterize those digraphs that are the acyclic intersection digraphs of subtrees of a directed tree. This is accomplished using the semilattice of subtrees of a rooted tree and the reachability relation.
Citation
Frank Harary, Jerald A.Kabell, ER. McMorris. Subtree Acyclic Digraphs[J], Ars Combinatoria, Volume 034. 93-95. .