Monochromatic paths and monochromatic cycles in edge-coloured k-partite tournaments
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A subdigraph H of D is called monochromatic if all of its arcs are coloured alike. A set N subset of V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) For ever...
| 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:11154/192 |
| Acceso en línea: | http://hdlhandlenet/123456789/169 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics kernel kernel by monochromatic paths k-partite tournament |
| Sumario: | We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A subdigraph H of D is called monochromatic if all of its arcs are coloured alike. A set N subset of V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) For every pair of different vertices u, v is an element of N there is no monochromatic directed path between them. (ii) For every vertex x is an element of V(D) N, there is a vertex y is an element of N such that there is an xy-monochromatic directed path. In this paper it is proved that if D is an m-coloured k-partite tournament such that every directed cycle of length 3 and every directed cycle of length 4 is monochromatic, then D has a kernel by monochromatic paths. Some previous results are generalized. |
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