Counterexample to a conjecture on edge-coloured tournaments
We call the tournament T an m-coloured tournament if the arcs of T are coloured with m colours. In this paper we prove that for each n greater than or equal to 6, there exists a 4-coloured tournament T-n of order n satisfying the two following conditions: (1) T-n does not contain C-3 (the directed c...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2004 |
| 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:11154/3225 |
| Acceso en línea: | http://hdl.handle.net/11154/3225 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics edge coloured tournament monochromatic directed path |
| Sumario: | We call the tournament T an m-coloured tournament if the arcs of T are coloured with m colours. In this paper we prove that for each n greater than or equal to 6, there exists a 4-coloured tournament T-n of order n satisfying the two following conditions: (1) T-n does not contain C-3 (the directed cycle of length 3, whose arcs are coloured with three distinct colours), and (2) T-n does not contain any vertex v such that for every other vertex x of T-n there is a monochromatic directed path from x to v. This answers a question proposed by Shen Minggang in 1988. (C) 2004 Elsevier B.V. All rights reserved. |
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