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 gra...

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Detalles Bibliográficos
Autores: Gutiérrez, Marisa, Leveque, Benjamín, Tondato, Silvia B.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:Argentina
Institución:Universidad Nacional de La Plata
Repositorio:SEDICI (UNLP)
Idioma:inglés
OAI Identifier:oai:sedici.unlp.edu.ar:10915/85929
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/85929
Access Level:acceso abierto
Palabra clave:Matemática
Asteroidal quadruples
Clique trees
Rooted path graphs
Descripción
Sumario: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 find such characterizations for rooted path graphs. For this purpose, we are studying in this paper directed path graphs that are non rooted path graphs. We prove that such graphs always contain an asteroidal quadruple.