Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs
A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum cliqu...
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2008
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paper:paper_0166218X_v156_n7_p1058_Bonomo2023-06-08T15:15:27Z Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs Bonomo, Flavia Durán, Guillermo A. Claw-free graphs Clique-perfect graphs Hereditary clique-Helly graphs Line graphs Perfect graphs Image processing Mathematical models Number theory Problem solving Set theory Claw free graphs Clique perfect graphs Hereditary clique-Helly graphs Line graphs Perfect graphs Graph theory A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum clique-independent set of G, respectively. A graph G is clique-perfect if these two numbers are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known. In this paper, we present a partial result in this direction; that is, we characterize clique-perfect graphs by a restricted list of forbidden induced subgraphs when the graph belongs to two different subclasses of claw-free graphs. © 2007 Elsevier B.V. All rights reserved. Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Durán, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v156_n7_p1058_Bonomo http://hdl.handle.net/20.500.12110/paper_0166218X_v156_n7_p1058_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 |
Claw-free graphs Clique-perfect graphs Hereditary clique-Helly graphs Line graphs Perfect graphs Image processing Mathematical models Number theory Problem solving Set theory Claw free graphs Clique perfect graphs Hereditary clique-Helly graphs Line graphs Perfect graphs Graph theory |
| spellingShingle |
Claw-free graphs Clique-perfect graphs Hereditary clique-Helly graphs Line graphs Perfect graphs Image processing Mathematical models Number theory Problem solving Set theory Claw free graphs Clique perfect graphs Hereditary clique-Helly graphs Line graphs Perfect graphs Graph theory Bonomo, Flavia Durán, Guillermo A. Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs |
| topic_facet |
Claw-free graphs Clique-perfect graphs Hereditary clique-Helly graphs Line graphs Perfect graphs Image processing Mathematical models Number theory Problem solving Set theory Claw free graphs Clique perfect graphs Hereditary clique-Helly graphs Line graphs Perfect graphs Graph theory |
| description |
A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum clique-independent set of G, respectively. A graph G is clique-perfect if these two numbers are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known. In this paper, we present a partial result in this direction; that is, we characterize clique-perfect graphs by a restricted list of forbidden induced subgraphs when the graph belongs to two different subclasses of claw-free graphs. © 2007 Elsevier B.V. All rights reserved. |
| author |
Bonomo, Flavia Durán, Guillermo A. |
| author_facet |
Bonomo, Flavia Durán, Guillermo A. |
| author_sort |
Bonomo, Flavia |
| title |
Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs |
| title_short |
Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs |
| title_full |
Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs |
| title_fullStr |
Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs |
| title_full_unstemmed |
Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs |
| title_sort |
partial characterizations of clique-perfect graphs i: subclasses of claw-free graphs |
| publishDate |
2008 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v156_n7_p1058_Bonomo http://hdl.handle.net/20.500.12110/paper_0166218X_v156_n7_p1058_Bonomo |
| work_keys_str_mv |
AT bonomoflavia partialcharacterizationsofcliqueperfectgraphsisubclassesofclawfreegraphs AT duranguillermoa partialcharacterizationsofcliqueperfectgraphsisubclassesofclawfreegraphs |
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1768543176156512256 |