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The forbidden subgraph characterization of directed vertex graphs. (English) Zbl 0928.05029
For a family \(F\) of non-empty sets, an undirected graph \(G\) is an intersection graph for \(F\) if there is a one-to-one correspondence between vertices of \(G\) and the sets of \(F\) such that two vertices in \(G\) are adjacent if and only if the corresponding sets in \(F\) have a non-empty intersection. A graph is a directed vertex graph or a directed path graph if it is the intersection graph of a family of directed paths in a directed tree. The author gives a characterization of directed vertex graphs based on 15 forbidden subgraphs.

MSC:
05C20 Directed graphs (digraphs), tournaments
05C75 Structural characterization of families of graphs
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