Graph classes with and without powers of bounded clique-width

• Autores: Bonomo, Flavia; Grippo, Luciano Norberto; Milanič, Martin; Safe, Martín D.
• Año de publicación: 2016
• Idioma: inglés
• Tipo de recurso: artículo
• Fuente: Discrete Applied Mathematics. 1-2016; (199): 3-15; http://www.sciencedirect.com/science/article/pii/S0166218X15002966
• Materia: Clique-width; Power of a graph; Hereditary graph class; Power-bounded clique-width; Ciencias de la Computación; Ciencias de la Computación e Información; Matemática Pura
• Institución: Universidad Nacional de General Sarmiento

Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Bonomo, Flavia. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.
Fil: Safe, Martín D. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Milanič, Martin. Universidad de Primorska; Eslovenia.
We initiate the study of graph classes of power-bounded clique-width, that is, graph classes for which there exist integers k and ℓ such that the kth powers of the graphs are of cliquewidth at most ℓ. We give sufficient and necessary conditions for this property. As our main results, we characterize graph classes of power-bounded clique-width within classes defined by either one forbidden induced subgraph, or by two connected forbidden induced subgraphs. We also show that for every positive integer k, there exists a graph class such that the kth powers of graphs in the class form a class of bounded clique-width, while this is not the case for any smaller power.