The number of (C-3)over right arrow-free vertices on 3-partite tournaments
Let T be a 3-partite tournament. We say that a vertex u is (C-3) over right arrow -free if v does not lie on any directed triangle of T. Let F-3 (T) be the set of the (C-3) over right arrow -free vertices in a 3-partite tournament and f(3)(T) its cardinality. In this paper we prove that if T is a re...
| 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:11154/234 |
| Acceso en línea: | http://hdlhandlenet/123456789/204 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics Directed triangle free vertex Regular 3-partite tournament |
| Sumario: | Let T be a 3-partite tournament. We say that a vertex u is (C-3) over right arrow -free if v does not lie on any directed triangle of T. Let F-3 (T) be the set of the (C-3) over right arrow -free vertices in a 3-partite tournament and f(3)(T) its cardinality. In this paper we prove that if T is a regular 3-partite tournament, then F-3 (T) must be contained in one of the partite sets of T. It is also shown that for every regular 3-partite tournament, f(3)(T) does not exceed n/9, where n is the order of T. On the other hand, we give an infinite family of strongly connected tournaments having n - 4 (C-3) over right arrow -free vertices. Finally we prove that for every c >= 3 there exists an infinite family of strongly connected c-partite tournaments, D-c(T), with n - c 1 (C-3) over right arrow -free vertices. (C) 2010 Elsevier B.V. All rights reserved. |
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