A Bang-Jensen-Gutin-Li type condition for pancyclicity in digraphs

Bang-Jensen-Gutin-Li type conditions are degree conditions for the existence of hamiltonian cycles in digraphs, which impose degree restrictions on nonadjacent vertices which have a common in-neighbor or a common out-neighbor. They can be viewed as directed analogues of both Fan-type conditions and heavy subgraph conditions in undirected graphs, and they also generalized the classes of locally semicomplete digrahs, loclaly in-semicomplete digraphs, and locally out-semicomplete digraphs. In this paper, we prove what is, to our knowledge, the first Bang-Jensen-Gutin-Li type condition for pancyclicity in digraphs. More precisely, let $D$ be a strong digraph with order $n\ge 3$. We show that, if for every $u\in V(D)$ belonging to a dominated nonadjacent pair or a dominating nonadjacent pair, we have $d(u)\ge n$, then $D$ is pancyclic, unless $D$ belongs to one of two well-characterized classes of exceptional digraphs.