Clique-perfectness and balancedness of some graph classes
A graph is clique-perfect if the maximum size of a clique-independent set (a set of pairwise disjoint maximal cliques) and the minimum size of a clique-transversal set (a set of vertices meeting every maximal clique) coincide for each induced subgraph. A graph is balanced if its clique-matrix contai...
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paper:paper_00207160_v91_n10_p2118_Bonomo2023-06-08T14:41:23Z Clique-perfectness and balancedness of some graph classes Bonomo, Flavia Durán, Guillermo A. Safe, Martín Darío balanced graphs clique-perfect graphs diamond-free graphs P4-tidy graphs paw-free graphs recognition algorithms Clustering algorithms Diamonds Graphic methods Polynomial approximation Balanced graphs Diamond-free graphs Free graphs Perfect graph Recognition algorithm Graph theory A graph is clique-perfect if the maximum size of a clique-independent set (a set of pairwise disjoint maximal cliques) and the minimum size of a clique-transversal set (a set of vertices meeting every maximal clique) coincide for each induced subgraph. A graph is balanced if its clique-matrix contains no square submatrix of odd size with exactly two ones per row and column. In this work, we give linear-time recognition algorithms and minimal forbidden induced subgraph characterizations of clique-perfectness and balancedness of P4-tidy graphs and a linear-time algorithm for computing a maximum clique-independent set and a minimum clique-transversal set for any P4-tidy graph. We also give a minimal forbidden induced subgraph characterization and a linear-time recognition algorithm for balancedness of paw-free graphs. Finally, we show that clique-perfectness of diamond-free graphs can be decided in polynomial time by showing that a diamond-free graph is clique-perfect if and only if it is balanced. © 2014, © 2014 Taylor & Francis. 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. Fil:Safe, M.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207160_v91_n10_p2118_Bonomo http://hdl.handle.net/20.500.12110/paper_00207160_v91_n10_p2118_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 |
balanced graphs clique-perfect graphs diamond-free graphs P4-tidy graphs paw-free graphs recognition algorithms Clustering algorithms Diamonds Graphic methods Polynomial approximation Balanced graphs Diamond-free graphs Free graphs Perfect graph Recognition algorithm Graph theory |
| spellingShingle |
balanced graphs clique-perfect graphs diamond-free graphs P4-tidy graphs paw-free graphs recognition algorithms Clustering algorithms Diamonds Graphic methods Polynomial approximation Balanced graphs Diamond-free graphs Free graphs Perfect graph Recognition algorithm Graph theory Bonomo, Flavia Durán, Guillermo A. Safe, Martín Darío Clique-perfectness and balancedness of some graph classes |
| topic_facet |
balanced graphs clique-perfect graphs diamond-free graphs P4-tidy graphs paw-free graphs recognition algorithms Clustering algorithms Diamonds Graphic methods Polynomial approximation Balanced graphs Diamond-free graphs Free graphs Perfect graph Recognition algorithm Graph theory |
| description |
A graph is clique-perfect if the maximum size of a clique-independent set (a set of pairwise disjoint maximal cliques) and the minimum size of a clique-transversal set (a set of vertices meeting every maximal clique) coincide for each induced subgraph. A graph is balanced if its clique-matrix contains no square submatrix of odd size with exactly two ones per row and column. In this work, we give linear-time recognition algorithms and minimal forbidden induced subgraph characterizations of clique-perfectness and balancedness of P4-tidy graphs and a linear-time algorithm for computing a maximum clique-independent set and a minimum clique-transversal set for any P4-tidy graph. We also give a minimal forbidden induced subgraph characterization and a linear-time recognition algorithm for balancedness of paw-free graphs. Finally, we show that clique-perfectness of diamond-free graphs can be decided in polynomial time by showing that a diamond-free graph is clique-perfect if and only if it is balanced. © 2014, © 2014 Taylor & Francis. |
| author |
Bonomo, Flavia Durán, Guillermo A. Safe, Martín Darío |
| author_facet |
Bonomo, Flavia Durán, Guillermo A. Safe, Martín Darío |
| author_sort |
Bonomo, Flavia |
| title |
Clique-perfectness and balancedness of some graph classes |
| title_short |
Clique-perfectness and balancedness of some graph classes |
| title_full |
Clique-perfectness and balancedness of some graph classes |
| title_fullStr |
Clique-perfectness and balancedness of some graph classes |
| title_full_unstemmed |
Clique-perfectness and balancedness of some graph classes |
| title_sort |
clique-perfectness and balancedness of some graph classes |
| publishDate |
2014 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207160_v91_n10_p2118_Bonomo http://hdl.handle.net/20.500.12110/paper_00207160_v91_n10_p2118_Bonomo |
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AT bonomoflavia cliqueperfectnessandbalancednessofsomegraphclasses AT duranguillermoa cliqueperfectnessandbalancednessofsomegraphclasses AT safemartindario cliqueperfectnessandbalancednessofsomegraphclasses |
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