Computational complexity of classical problems for hereditary clique-helly graphs

Detalhes bibliográficos
Autor(a) principal: Bonomo,Flavia
Data de Publicação: 2004
Outros Autores: Durán,Guillermo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Pesquisa operacional (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382004000300006
Resumo: A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of them can be deduced easily by known results. We prove that the clique-covering problem remains NP-complete for hereditary clique-Helly graphs. Furthermore, the decision problems associated to the clique-transversal and the clique-independence numbers are analyzed too. We prove that they remain NP-complete for a smaller class: hereditary clique-Helly split graphs.
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spelling Computational complexity of classical problems for hereditary clique-helly graphscomputational complexityhereditary clique-Helly graphssplit graphsA graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of them can be deduced easily by known results. We prove that the clique-covering problem remains NP-complete for hereditary clique-Helly graphs. Furthermore, the decision problems associated to the clique-transversal and the clique-independence numbers are analyzed too. We prove that they remain NP-complete for a smaller class: hereditary clique-Helly split graphs.Sociedade Brasileira de Pesquisa Operacional2004-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382004000300006Pesquisa Operacional v.24 n.3 2004reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/S0101-74382004000300006info:eu-repo/semantics/openAccessBonomo,FlaviaDurán,Guillermoeng2005-02-10T00:00:00Zoai:scielo:S0101-74382004000300006Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2005-02-10T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false
dc.title.none.fl_str_mv Computational complexity of classical problems for hereditary clique-helly graphs
title Computational complexity of classical problems for hereditary clique-helly graphs
spellingShingle Computational complexity of classical problems for hereditary clique-helly graphs
Bonomo,Flavia
computational complexity
hereditary clique-Helly graphs
split graphs
title_short Computational complexity of classical problems for hereditary clique-helly graphs
title_full Computational complexity of classical problems for hereditary clique-helly graphs
title_fullStr Computational complexity of classical problems for hereditary clique-helly graphs
title_full_unstemmed Computational complexity of classical problems for hereditary clique-helly graphs
title_sort Computational complexity of classical problems for hereditary clique-helly graphs
author Bonomo,Flavia
author_facet Bonomo,Flavia
Durán,Guillermo
author_role author
author2 Durán,Guillermo
author2_role author
dc.contributor.author.fl_str_mv Bonomo,Flavia
Durán,Guillermo
dc.subject.por.fl_str_mv computational complexity
hereditary clique-Helly graphs
split graphs
topic computational complexity
hereditary clique-Helly graphs
split graphs
description A graph is clique-Helly when its cliques satisfy the Helly property. A graph is hereditary clique-Helly when every induced subgraph of it is clique-Helly. The decision problems associated to the stability, chromatic, clique and clique-covering numbers are NP-complete for clique-Helly graphs. In this note, we analyze the complexity of these problems for hereditary clique-Helly graphs. Some of them can be deduced easily by known results. We prove that the clique-covering problem remains NP-complete for hereditary clique-Helly graphs. Furthermore, the decision problems associated to the clique-transversal and the clique-independence numbers are analyzed too. We prove that they remain NP-complete for a smaller class: hereditary clique-Helly split graphs.
publishDate 2004
dc.date.none.fl_str_mv 2004-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382004000300006
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382004000300006
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-74382004000300006
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
publisher.none.fl_str_mv Sociedade Brasileira de Pesquisa Operacional
dc.source.none.fl_str_mv Pesquisa Operacional v.24 n.3 2004
reponame:Pesquisa operacional (Online)
instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron:SOBRAPO
instname_str Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
instacron_str SOBRAPO
institution SOBRAPO
reponame_str Pesquisa operacional (Online)
collection Pesquisa operacional (Online)
repository.name.fl_str_mv Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)
repository.mail.fl_str_mv ||sobrapo@sobrapo.org.br
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