Chronological Rectangle Digraphs

Interval graphs admit elegant ordering and structural characterizations. A natural digraph analogue of interval graphs, called chronological interval digraphs, has recently been identified and studied. In this paper, we introduce the class of chronological rectangle digraphs, a generalization of chronological interval digraphs. We show that several properties of chronological interval digraphs extend to this larger class of digraphs. We also show that chronological rectangle digraphs are all weakly clustered. Finally we give an ordering characterization of chronological rectangle digraphs, akin to that of chronological interval digraphs, which generalizes the usual ordering characterization of interval graphs.