On edge transitivity of directed graphs (Q1894773)

The author calls a graph \(G\) a local comparability graph if its edges can be given an acyclic orientation such that for each arc \(uv\), the subgraph induced by the nodes that are simultaneously ancestors of \(v\) and descendants of \(u\) is transitive. He then defines a parameter called the dimension of the graph and shows that a local comparability graph has dimension one if and only if it is a connected proper interval graph. He also gives a new characterization of circle graphs in terms of edge transitivity.