Special asteroidal quadruple on directed path graph non rooted path graph

• Autores: Gutierrez, M.; Tondato, Silvia Beatriz
• Año de publicación: 2013
• Idioma: inglés
• Tipo de recurso: documento de conferencia
• Materia: Ciencias Informáticas; Asteroidal quadruples; Forbidden subgraphs
• Institución: Universidad Nacional de La Plata

An asteroidal triple in a graph G is a set of three non- adjacent vertices such that for any two of them there exists a path be- tween them that does not intersect the neighborhood of the third. Special asteroidal triple in a graph G is an asteroidal triple such that each pair is linked by a special connection. A special asteroidal triples play a central role in a characterization of directed path graphs by Cameron, Hoáng and Lévêque. They also introduce a related notion of asteroidal quadru- ple and conjecture a characterization of rooted path graphs. In its original form this conjecture is not complete, still in leafage four, as was showed in. But, as suggested by the conjecture, a characterization by forbidding particular types of asteroidal quadruples may hold. We prove that the conjecture in the original form is true on directed path graphs with leafage four having two minimal separators with multiplicity two. Thus we build the family of forbidden subgraphs in this case.
Sociedad Argentina de Informática e Investigación Operativa