On the convex hull of 3-cycles of the complete graph
Autor(a) principal: | |
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Data de Publicação: | 2003 |
Outros Autores: | , |
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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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 |
_version_ |
1750318016237666304 |