Representing digraphs using intervals or circular arcs

Containment and overlap representations of digraphs are studied, with the following results. The interval containment digraphs are the digraphs of Ferrers dimension 2, and the circular-arc containment digraphs are the complements of circular-arc intersection digraphs. A poset is an interval containment poset if and only if its comparability digraph is an interval containment digraph, and a graph is an interval graph if and only if the corresponding symmetric digraph with loops is an interval digraph. In an appropriate model of overlap representation using intervals, the unit right-overlap interval digraphs are precisely the unit interval digraphs, and the adjacency matrices of right-overlap interval digraphs have a simple structural characterization bounding their Ferrers dimension by 3.