On clique‐inverse graphs of graphs with bounded clique number
- Autores
- Alcón, Liliana Graciela; Gravier, Sylvain; Linhares Sales, Cláudia; Protti, Fábio; Ravenna, Gabriela Susana
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The clique graph K(G) of G is the intersection graph of the family of maximal cliques of G. For a family F of graphs, the family of clique-inverse graphs of F, denoted by K−1(F), is defined as K−1(F) = {H|K(H) ∈ F}. Let F p be the family of Kp-free graphs, that is, graphs with clique number at most p − 1, for an integer constant p ≥ 2. Deciding whether a graph H is a clique-inverse graph of F p can be done in polynomial time; in addition, for p ∈ {2, 3, 4}, K − 1 (Fp) can be characterized by a finite family of forbidden induced subgraphs. In Protti and Szwarcfiter, the authors propose to extend such characterizations to higher values of p. Then a natural question arises: Is there a characterization of K − 1 (Fp) by means of a finite family of forbidden induced subgraphs, for any p ≥ 2? In this note we give a positive answer to this question. We present upper bounds for the order, the clique number, and the stability number of every forbidden induced subgraph for K − 1 (Fp) in terms of p.
Facultad de Ciencias Exactas - Materia
-
Matemática
clique graph
clique-inverse graph - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-nd/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/129017
Ver los metadatos del registro completo
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On clique‐inverse graphs of graphs with bounded clique numberAlcón, Liliana GracielaGravier, SylvainLinhares Sales, CláudiaProtti, FábioRavenna, Gabriela SusanaMatemáticaclique graphclique-inverse graphThe clique graph K(G) of G is the intersection graph of the family of maximal cliques of G. For a family F of graphs, the family of clique-inverse graphs of F, denoted by K−1(F), is defined as K−1(F) = {H|K(H) ∈ F}. Let F p be the family of Kp-free graphs, that is, graphs with clique number at most p − 1, for an integer constant p ≥ 2. Deciding whether a graph H is a clique-inverse graph of F p can be done in polynomial time; in addition, for p ∈ {2, 3, 4}, K − 1 (Fp) can be characterized by a finite family of forbidden induced subgraphs. In Protti and Szwarcfiter, the authors propose to extend such characterizations to higher values of p. Then a natural question arises: Is there a characterization of K − 1 (Fp) by means of a finite family of forbidden induced subgraphs, for any p ≥ 2? In this note we give a positive answer to this question. We present upper bounds for the order, the clique number, and the stability number of every forbidden induced subgraph for K − 1 (Fp) in terms of p.Facultad de Ciencias Exactas2020-01-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf531-538http://sedici.unlp.edu.ar/handle/10915/129017enginfo:eu-repo/semantics/altIdentifier/issn/0364-9024info:eu-repo/semantics/altIdentifier/issn/1097-0118info:eu-repo/semantics/altIdentifier/doi/10.1002/jgt.22544info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-nd/4.0/Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T11:03:09Zoai:sedici.unlp.edu.ar:10915/129017Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 11:03:09.432SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
On clique‐inverse graphs of graphs with bounded clique number |
| title |
On clique‐inverse graphs of graphs with bounded clique number |
| spellingShingle |
On clique‐inverse graphs of graphs with bounded clique number Alcón, Liliana Graciela Matemática clique graph clique-inverse graph |
| title_short |
On clique‐inverse graphs of graphs with bounded clique number |
| title_full |
On clique‐inverse graphs of graphs with bounded clique number |
| title_fullStr |
On clique‐inverse graphs of graphs with bounded clique number |
| title_full_unstemmed |
On clique‐inverse graphs of graphs with bounded clique number |
| title_sort |
On clique‐inverse graphs of graphs with bounded clique number |
| dc.creator.none.fl_str_mv |
Alcón, Liliana Graciela Gravier, Sylvain Linhares Sales, Cláudia Protti, Fábio Ravenna, Gabriela Susana |
| author |
Alcón, Liliana Graciela |
| author_facet |
Alcón, Liliana Graciela Gravier, Sylvain Linhares Sales, Cláudia Protti, Fábio Ravenna, Gabriela Susana |
| author_role |
author |
| author2 |
Gravier, Sylvain Linhares Sales, Cláudia Protti, Fábio Ravenna, Gabriela Susana |
| author2_role |
author author author author |
| dc.subject.none.fl_str_mv |
Matemática clique graph clique-inverse graph |
| topic |
Matemática clique graph clique-inverse graph |
| dc.description.none.fl_txt_mv |
The clique graph K(G) of G is the intersection graph of the family of maximal cliques of G. For a family F of graphs, the family of clique-inverse graphs of F, denoted by K−1(F), is defined as K−1(F) = {H|K(H) ∈ F}. Let F p be the family of Kp-free graphs, that is, graphs with clique number at most p − 1, for an integer constant p ≥ 2. Deciding whether a graph H is a clique-inverse graph of F p can be done in polynomial time; in addition, for p ∈ {2, 3, 4}, K − 1 (Fp) can be characterized by a finite family of forbidden induced subgraphs. In Protti and Szwarcfiter, the authors propose to extend such characterizations to higher values of p. Then a natural question arises: Is there a characterization of K − 1 (Fp) by means of a finite family of forbidden induced subgraphs, for any p ≥ 2? In this note we give a positive answer to this question. We present upper bounds for the order, the clique number, and the stability number of every forbidden induced subgraph for K − 1 (Fp) in terms of p. Facultad de Ciencias Exactas |
| description |
The clique graph K(G) of G is the intersection graph of the family of maximal cliques of G. For a family F of graphs, the family of clique-inverse graphs of F, denoted by K−1(F), is defined as K−1(F) = {H|K(H) ∈ F}. Let F p be the family of Kp-free graphs, that is, graphs with clique number at most p − 1, for an integer constant p ≥ 2. Deciding whether a graph H is a clique-inverse graph of F p can be done in polynomial time; in addition, for p ∈ {2, 3, 4}, K − 1 (Fp) can be characterized by a finite family of forbidden induced subgraphs. In Protti and Szwarcfiter, the authors propose to extend such characterizations to higher values of p. Then a natural question arises: Is there a characterization of K − 1 (Fp) by means of a finite family of forbidden induced subgraphs, for any p ≥ 2? In this note we give a positive answer to this question. We present upper bounds for the order, the clique number, and the stability number of every forbidden induced subgraph for K − 1 (Fp) in terms of p. |
| publishDate |
2020 |
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2020-01-28 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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eng |
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eng |
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