A classification of all arc-locally semicomplete digraphs

Arc-locally semicomplete digraphs were introduced by Bang-Jensen as a common generalization of both semicomplete and semicomplete bipartite digraphs in 1993. Later, Bang-Jensen (2004), Galeana-Sánchez and Goldfeder (2009) and Wang and Wang (2009) provided a characterization of strong arc-locally semicomplete digraphs. In this paper, we provide a characterization of strong and non-strong arc-locally semicomplete digraphs which generalizes some results by Bang-Jensen.