Kernels in pretransitive digraphs
Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. A kernel N of D is an independent set of vertices such that for every w is an element of V(D) - N there exists an are from w to N. A digraph D is called right-pretransitive (resp. left-pretransitive) when...
| Autores: | , |
|---|---|
| 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:11154/1642 |
| Acceso en línea: | http://hdl.handle.net/11154/1642 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics kernel kernel-perfect digraph right-pretransitive digraph left-pretransitive digraph |
| Sumario: | Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. A kernel N of D is an independent set of vertices such that for every w is an element of V(D) - N there exists an are from w to N. A digraph D is called right-pretransitive (resp. left-pretransitive) when (u, v) is an element of A(D) and (v, w) is an element of A(D) implies (u, w) is an element of A(D) or (w, v) is an element of A(D) (resp. (u, v) is an element of A(D) and (v, w) is an element of A(D) implies (u, w) is an element of A(D) or (v, u) is an element of A(D)). This concepts were introduced by P. Duchet in 1980. In this paper is proved the following result: Let D be a digraph. If D = D-1 boolean OR D-2 where D-1 is a right-pretransitive digraph, D-2 is a left-pretransitive digraph and D-i contains no infinite outward path for i is an element of {1, 2}, then D has a kernel. (C) 2003 Elsevier B.V. All rights reserved. |
|---|