On the structure of strong 3-quasi-transitive digraphs
In this paper, D = (V (D), A(D)) denotes a loopless directed graph (digraph) with at most one arc from u to v for every pair of vertices u and v of V (D). Given a digraph D, we say that D is 3-quasi-transitive if, whenever u -> v -> w -> z in D, then u and z are adjacent or u = z. In Bang-J...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2010 |
| País: | México |
| Institución: | Universidad Nacional Autónoma de México |
| Repositorio: | Sistema de Información de la Facultad de Ciencias, UNAM |
| OAI Identifier: | oai:repositorio.fciencias.unam.mx:11154/235 |
| Acceso en línea: | http://hdlhandlenet/123456789/224 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics 3-quasi-transitive digraphs Arc-locally semicomplete digraphs Generalization of tournaments Hamiltonian digraphs |
| Sumario: | In this paper, D = (V (D), A(D)) denotes a loopless directed graph (digraph) with at most one arc from u to v for every pair of vertices u and v of V (D). Given a digraph D, we say that D is 3-quasi-transitive if, whenever u -> v -> w -> z in D, then u and z are adjacent or u = z. In Bang-Jensen (2004)[3], Bang-Jensen introduced 3-quasi-transitive digraphs and claimed that the only strong 3-quasi-transitive digraphs are the strong semicomplete digraphs and strong semicomplete bipartite digraphs. In this paper, we exhibit a family of strong 3-quasi-transitive digraphs distinct from strong semicomplete digraphs and strong semicomplete bipartite digraphs and provide a complete characterization of strong 3-quasi-transitive digraphs. (C) 2010 Elsevier B.V. All rights reserved. |
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