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By using modular decomposition and handling certain graph operations such as join and union, we show that the Generalized Limited Packing Problem—NP-complete in general—can be solved in polynomial time in some graph classes with a limited number of P4-partners; specifically P4-tidy graphs, which contain cographs and P4-sparse graphs. In particular, we describe an algorithm to compute the associated numbers in polynomial time within these graph classes. In this way, we generalize some of the previous results on the subject. We also make some progress on the study of the computational complexity of the Generalized Multiple Domination Problem in graphs. Fil: Dobson, M. P.. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; Argentina Fil: Hinrichsen, E.. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; Argentina Fil: Leoni, Valeria Alejandra. Universidad Nacional de Rosario. Facultad de Cs.exactas Ingenieria y Agrimensura. Escuela de Cs.exactas y Naturales. Departamento de Matematica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Cientifico Tecnológico Rosario; Argentina |
