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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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##### References:
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