Graph classes with and without powers of bounded clique-width

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 clique-width at most ℓ. We give sufficient and necessary conditions for this property. As our main results, we characteriz...

ver descrição completa

Detalhes bibliográficos
Autores: Bonomo, Flavia, Grippo, Luciano Norberto, Milanič, Martin, Safe, Martin Dario
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2016
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/55546
Acesso em linha:http://hdl.handle.net/11336/55546
Access Level:acceso abierto
Palavra-chave:Clique-Width
Hereditary Graph Class
Power of A Graph
Power-Bounded Clique-Width
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
https://purl.org/becyt/ford/1.1
Descrição
Resumo: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 clique-width 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.