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...
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2016
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v199_n_p3_Bonomo http://hdl.handle.net/20.500.12110/paper_0166218X_v199_n_p3_Bonomo |
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paper:paper_0166218X_v199_n_p3_Bonomo2023-06-08T15:15:34Z Graph classes with and without powers of bounded clique-width Bonomo, Flavia Grippo, Luciano Norberto Safe, Martín Darío Clique-width Hereditary graph class Power of a graph Power-bounded clique-width Combinatorial mathematics Clique-width Forbidden induced subgraphs Graph class Induced subgraphs Positive integers Power of a graph Sufficient and necessary condition Within class Graph theory 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. © 2015 Elsevier B.V. All rights reserved. Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Grippo, L.N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Safe, M.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v199_n_p3_Bonomo http://hdl.handle.net/20.500.12110/paper_0166218X_v199_n_p3_Bonomo |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Clique-width Hereditary graph class Power of a graph Power-bounded clique-width Combinatorial mathematics Clique-width Forbidden induced subgraphs Graph class Induced subgraphs Positive integers Power of a graph Sufficient and necessary condition Within class Graph theory |
| spellingShingle |
Clique-width Hereditary graph class Power of a graph Power-bounded clique-width Combinatorial mathematics Clique-width Forbidden induced subgraphs Graph class Induced subgraphs Positive integers Power of a graph Sufficient and necessary condition Within class Graph theory Bonomo, Flavia Grippo, Luciano Norberto Safe, Martín Darío Graph classes with and without powers of bounded clique-width |
| topic_facet |
Clique-width Hereditary graph class Power of a graph Power-bounded clique-width Combinatorial mathematics Clique-width Forbidden induced subgraphs Graph class Induced subgraphs Positive integers Power of a graph Sufficient and necessary condition Within class Graph theory |
| description |
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. © 2015 Elsevier B.V. All rights reserved. |
| author |
Bonomo, Flavia Grippo, Luciano Norberto Safe, Martín Darío |
| author_facet |
Bonomo, Flavia Grippo, Luciano Norberto Safe, Martín Darío |
| author_sort |
Bonomo, Flavia |
| title |
Graph classes with and without powers of bounded clique-width |
| title_short |
Graph classes with and without powers of bounded clique-width |
| title_full |
Graph classes with and without powers of bounded clique-width |
| title_fullStr |
Graph classes with and without powers of bounded clique-width |
| title_full_unstemmed |
Graph classes with and without powers of bounded clique-width |
| title_sort |
graph classes with and without powers of bounded clique-width |
| publishDate |
2016 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v199_n_p3_Bonomo http://hdl.handle.net/20.500.12110/paper_0166218X_v199_n_p3_Bonomo |
| work_keys_str_mv |
AT bonomoflavia graphclasseswithandwithoutpowersofboundedcliquewidth AT grippolucianonorberto graphclasseswithandwithoutpowersofboundedcliquewidth AT safemartindario graphclasseswithandwithoutpowersofboundedcliquewidth |
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1768542500128030720 |