Monochromatic paths and at most 2-coloured arc sets in edge-coloured tournaments
We call the tournament T an m-coloured tournament if the arcs of T are coloured with m-colours. If v is a vertex of an m- coloured tournament T, we denote by xi(v) the set of colours assigned to the arcs with v as an endpoint. In this paper is proved that if T is an m- coloured tournament with |xi(v...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| 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:11154/3204 |
| Acceso en línea: | http://hdl.handle.net/11154/3204 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics kernel kernel-perfect digraph kernel by monochromatic paths tournament m-coloured tournament |
| Sumario: | We call the tournament T an m-coloured tournament if the arcs of T are coloured with m-colours. If v is a vertex of an m- coloured tournament T, we denote by xi(v) the set of colours assigned to the arcs with v as an endpoint. In this paper is proved that if T is an m- coloured tournament with |xi(v)| <= 2 for each vertex v of T, and T satisfies at least one of the two following properties ( 1) m not equal 3 or ( 2) m = 3 and T contains no C-3 ( the directed cycle of length 3 whose arcs are coloured with three distinct colours). Then there is a vertex v of T such that for every other vertex x of T, there is a monochromatic directed path from x to v. |
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