The forbidden subgraph characterization of directed vertex graphs.

*(English)*Zbl 0928.05029For 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.

Reviewer: D.P.Brown (Carbondale)

##### MSC:

05C20 | Directed graphs (digraphs), tournaments |

05C75 | Structural characterization of families of graphs |

##### Keywords:

digraphs; intersection graph; directed vertex graph; directed path graph; characterization; forbidden subgraphs
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\textit{B. S. Panda}, Discrete Math. 196, No. 1--3, 239--256 (1999; Zbl 0928.05029)

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##### References:

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