Forbidden subgraph characterization of extended star directed path graphs that are not rooted directed path graphs
نویسندگان
چکیده
An asteroidal triple in a graph is a set of three non-adjacent vertices such that for any two of them there exists a path between them that does not intersect the neighborhood of the third. An asteroidal quadruple is a set of four non-adjacent vertices such that any three of them is an asteroidal triple. In this paper, we study a subclass of directed path graph, the class of extended star directed path graph i.e directed path graph which admits a directed model with exactly one vertex of degree at least three, and give a characterization for extended star directed path graphs non rooted directed path graphs in terms of asteroidal quadruples. As byproduct, we show the family of induced forbidden subgraphs for this class.
منابع مشابه
Asteroidal quadruples in non rooted path graphs
A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to ...
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