On the convex hull of 3-cycles of the complete graph

Detalhes bibliográficos
Autor(a) principal: Kovalev,Michel
Data de Publicação: 2003
Outros Autores: Maurras,Jean-François, Vaxès,Yann
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Pesquisa operacional (Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382003000100008
Resumo: Let Kn be the complete undirected graph with n vertices. A 3-cycle is a cycle consisting of 3 edges. The 3-cycle polytope is defined as the convex hull of the incidence vectors of all 3-cycles in Kn. In this paper, we present a polyhedral analysis of the 3-cycle polytope. In particular, we give several classes of facet defining inequalities of this polytope and we prove that the separation problem associated to one of these classes of inequalities is NP-complete. Finally, it is proved that the 3-cycle polytope is a 2-neighborly polytope.
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spelling On the convex hull of 3-cycles of the complete graphpolytopecyclefacetNP-completenessLet Kn be the complete undirected graph with n vertices. A 3-cycle is a cycle consisting of 3 edges. The 3-cycle polytope is defined as the convex hull of the incidence vectors of all 3-cycles in Kn. In this paper, we present a polyhedral analysis of the 3-cycle polytope. In particular, we give several classes of facet defining inequalities of this polytope and we prove that the separation problem associated to one of these classes of inequalities is NP-complete. Finally, it is proved that the 3-cycle polytope is a 2-neighborly polytope.Sociedade Brasileira de Pesquisa Operacional2003-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382003000100008Pesquisa Operacional v.23 n.1 2003reponame:Pesquisa operacional (Online)instname:Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)instacron:SOBRAPO10.1590/S0101-74382003000100008info:eu-repo/semantics/openAccessKovalev,MichelMaurras,Jean-FrançoisVaxès,Yanneng2003-05-26T00:00:00Zoai:scielo:S0101-74382003000100008Revistahttp://www.scielo.br/popehttps://old.scielo.br/oai/scielo-oai.php||sobrapo@sobrapo.org.br1678-51420101-7438opendoar:2003-05-26T00:00Pesquisa operacional (Online) - Sociedade Brasileira de Pesquisa Operacional (SOBRAPO)false
dc.title.none.fl_str_mv On the convex hull of 3-cycles of the complete graph
title On the convex hull of 3-cycles of the complete graph
spellingShingle On the convex hull of 3-cycles of the complete graph
Kovalev,Michel
polytope
cycle
facet
NP-completeness
title_short On the convex hull of 3-cycles of the complete graph
title_full On the convex hull of 3-cycles of the complete graph
title_fullStr On the convex hull of 3-cycles of the complete graph
title_full_unstemmed On the convex hull of 3-cycles of the complete graph
title_sort On the convex hull of 3-cycles of the complete graph
author Kovalev,Michel
author_facet Kovalev,Michel
Maurras,Jean-François
Vaxès,Yann
author_role author
author2 Maurras,Jean-François
Vaxès,Yann
author2_role author
author
dc.contributor.author.fl_str_mv Kovalev,Michel
Maurras,Jean-François
Vaxès,Yann
dc.subject.por.fl_str_mv polytope
cycle
facet
NP-completeness
topic polytope
cycle
facet
NP-completeness
description Let Kn be the complete undirected graph with n vertices. A 3-cycle is a cycle consisting of 3 edges. The 3-cycle polytope is defined as the convex hull of the incidence vectors of all 3-cycles in Kn. In this paper, we present a polyhedral analysis of the 3-cycle polytope. In particular, we give several classes of facet defining inequalities of this polytope and we prove that the separation problem associated to one of these classes of inequalities is NP-complete. Finally, it is proved that the 3-cycle polytope is a 2-neighborly polytope.
publishDate 2003
dc.date.none.fl_str_mv 2003-01-01
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=S0101-74382003000100008
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382003000100008
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0101-74382003000100008
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.23 n.1 2003
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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