About (k,l)-kernels, semikernels and Grundy functions in partial line digraphs
Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 = l = k, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial linedigraph LD. Moreover, if l < k and the girth of D is at least l+1, the...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/184855 |
| Acceso en línea: | https://hdl.handle.net/2117/184855 https://dx.doi.org/10.7151/dmgt.2104 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory digraphs in-domination kernel Grundy function. Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Sumario: | Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 = l = k, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial linedigraph LD. Moreover, if l < k and the girth of D is at least l+1, then these two numbers are equal. We also prove that the number of semikernels of D is equal to the number of semikernels of LD. Furthermore, we introduce the concept of (k, l)-Grundy function as a generalization of the concept of Grundy function and we prove that the number of (k, l)-Grundy functions of D is equal to the number of (k, l)-Grundy functions of any partial line digraph LD. |
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