About (k,l)-kernels, semikernels and Grundy functions in partial line digraphs
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
ProjectTECNICAS DE OPTIMIZACION EN TEORIA DE GRAFOS, GRUPOS Y COMBINATORIA. APLICACIONES A REDES, ALGORITMOS Y PROTOCOLOS DE COMUNICACION. (MINECO-MTM2014-60127-P)
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.
CitationBalbuena, C.; Galeana, H.; Guevara, N. About (k,l)-kernels, semikernels and Grundy functions in partial line digraphs. "Discussiones Mathematicae Graph Theory", Juny 2019, vol. 39, núm. 4, p. 855-866.
ISSNISSN 1234-3099 (print version) ISSN 2083-5892 (electronic version)