On clique‐inverse graphs of graphs with bounded clique number

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...

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Autores principales: Alcón, Liliana Graciela, Gravier, Sylvain, Linhares Sales, Cláudia, Protti, Fábio, Ravenna, Gabriela Susana
Formato: Articulo
Lenguaje:Inglés
Publicado: 2020
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Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/129017
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id I19-R120-10915-129017
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
clique graph
clique-inverse graph
spellingShingle Matemática
clique graph
clique-inverse graph
Alcón, Liliana Graciela
Gravier, Sylvain
Linhares Sales, Cláudia
Protti, Fábio
Ravenna, Gabriela Susana
On clique‐inverse graphs of graphs with bounded clique number
topic_facet Matemática
clique graph
clique-inverse graph
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.
format Articulo
Articulo
author Alcón, Liliana Graciela
Gravier, Sylvain
Linhares Sales, Cláudia
Protti, Fábio
Ravenna, Gabriela Susana
author_facet Alcón, Liliana Graciela
Gravier, Sylvain
Linhares Sales, Cláudia
Protti, Fábio
Ravenna, Gabriela Susana
author_sort Alcón, Liliana Graciela
title On clique‐inverse graphs of graphs with bounded clique number
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
publishDate 2020
url http://sedici.unlp.edu.ar/handle/10915/129017
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