A numbering of the vertices of special networks (Q1356750)

The paper characterizes acyclic digraphs which remain acyclic under a certain type of arc addition. The vertices of such digraphs admit a labelling \(f\) such that \(f(x)< f(y)\) and \(f(x)= f(z)\) whenever \((x,y)\) and \((x,z)\) are arcs of the digraph. The characterization is via a unique forbidden subgraph, which yields an acyclic digraph under a certain closure operation. The paper also develops an algorithm for constructing such functions.