A generalization of the helly property applied to the cliques of a graph
Autor(a) principal: | |
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Data de Publicação: | 2002 |
Outros Autores: | , |
Tipo de documento: | Relatório |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRJ |
Texto Completo: | http://hdl.handle.net/11422/1985 |
Resumo: | Let p ≥ 1 and q ≥ 0 be integers. A family S of sets is (p,q)-intersecting when every subfamily S' ⊆ S formed by p or less members has total intersection of cardinality at least q. A family F of sets is (p,q)-Helly when every (p,q)-intersecting subfamily F' ⊆ F has total intersection of cardinality at least q. A graph G is a (p, q)- clique-Helly graph when its family of cliques (maximal complete sets) is (P, q)-Helly. According to this terminology, the usual Helly property and the clique-Helly graphs correspond to the case p = 2, q = 1. In this work we present characterizations for (p,q)-Helly families of sets and (p,q)-clique-Helly graphs. For fixed p,q those characterizations lead to polynomial-time recognition algorithms. When p or q is not fixed, it is shown that the recognition of (p,q)-clique-Helly graphs is NP-hard. We also extend further the notions presented, by defining the (p,q, r)-Helly property (which holds when every (p, q)-intersecting subfamily F' ⊆ F has total intersection of cardinality at least r) and giving a way of recognizing (p, q, r)-Helly families in terms of the (p, q)-Helly property. |
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Dourado, Mitre CostaProtti, FábioSzwarcfiter, Jayme Luiz2017-05-12T14:03:31Z2023-11-30T03:00:28Z2002-12-31DOURADO, M. C. ; PROTTI, F. ; SZWARCFITER, J. L.A generalization of the helly property applied to the cliques of a graph. Rio de Janeiro: NCE, UFRJ, 2002. 25 p. (Relatório Técnico, 01/02)http://hdl.handle.net/11422/1985Let p ≥ 1 and q ≥ 0 be integers. A family S of sets is (p,q)-intersecting when every subfamily S' ⊆ S formed by p or less members has total intersection of cardinality at least q. A family F of sets is (p,q)-Helly when every (p,q)-intersecting subfamily F' ⊆ F has total intersection of cardinality at least q. A graph G is a (p, q)- clique-Helly graph when its family of cliques (maximal complete sets) is (P, q)-Helly. According to this terminology, the usual Helly property and the clique-Helly graphs correspond to the case p = 2, q = 1. In this work we present characterizations for (p,q)-Helly families of sets and (p,q)-clique-Helly graphs. For fixed p,q those characterizations lead to polynomial-time recognition algorithms. When p or q is not fixed, it is shown that the recognition of (p,q)-clique-Helly graphs is NP-hard. We also extend further the notions presented, by defining the (p,q, r)-Helly property (which holds when every (p, q)-intersecting subfamily F' ⊆ F has total intersection of cardinality at least r) and giving a way of recognizing (p, q, r)-Helly families in terms of the (p, q)-Helly property.Submitted by Elaine Almeida (elaine.almeida@nce.ufrj.br) on 2017-05-12T14:03:31Z No. of bitstreams: 1 01_02_000613309.pdf: 2403777 bytes, checksum: 811db86cf0e11b2f094e8974a3c519d2 (MD5)Made available in DSpace on 2017-05-12T14:03:31Z (GMT). No. of bitstreams: 1 01_02_000613309.pdf: 2403777 bytes, checksum: 811db86cf0e11b2f094e8974a3c519d2 (MD5) Previous issue date: 2002-12-31engRelatório Técnico NCECNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAOGrafo cliqueTeoria dos grafosA generalization of the helly property applied to the cliques of a graphinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/report0102abertoBrasilInstituto Tércio Pacitti de Aplicações e Pesquisas Computacionaisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJORIGINAL01_02_000613309.pdf01_02_000613309.pdfapplication/pdf1227739http://pantheon.ufrj.br:80/bitstream/11422/1985/3/01_02_000613309.pdfb987ae6d85fc6ad2cf71e04b3929a5cdMD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81853http://pantheon.ufrj.br:80/bitstream/11422/1985/2/license.txtdd32849f2bfb22da963c3aac6e26e255MD52TEXT01_02_000613309.pdf.txt01_02_000613309.pdf.txtExtracted texttext/plain38377http://pantheon.ufrj.br:80/bitstream/11422/1985/4/01_02_000613309.pdf.txt035d660becc457fa6ab1233379035434MD5411422/19852023-11-30 00:00:28.739oai:pantheon.ufrj.br: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Repositório de PublicaçõesPUBhttp://www.pantheon.ufrj.br/oai/requestopendoar:2023-11-30T03:00:28Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false |
dc.title.en.fl_str_mv |
A generalization of the helly property applied to the cliques of a graph |
title |
A generalization of the helly property applied to the cliques of a graph |
spellingShingle |
A generalization of the helly property applied to the cliques of a graph Dourado, Mitre Costa CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Grafo clique Teoria dos grafos |
title_short |
A generalization of the helly property applied to the cliques of a graph |
title_full |
A generalization of the helly property applied to the cliques of a graph |
title_fullStr |
A generalization of the helly property applied to the cliques of a graph |
title_full_unstemmed |
A generalization of the helly property applied to the cliques of a graph |
title_sort |
A generalization of the helly property applied to the cliques of a graph |
author |
Dourado, Mitre Costa |
author_facet |
Dourado, Mitre Costa Protti, Fábio Szwarcfiter, Jayme Luiz |
author_role |
author |
author2 |
Protti, Fábio Szwarcfiter, Jayme Luiz |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Dourado, Mitre Costa Protti, Fábio Szwarcfiter, Jayme Luiz |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
topic |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO Grafo clique Teoria dos grafos |
dc.subject.por.fl_str_mv |
Grafo clique Teoria dos grafos |
description |
Let p ≥ 1 and q ≥ 0 be integers. A family S of sets is (p,q)-intersecting when every subfamily S' ⊆ S formed by p or less members has total intersection of cardinality at least q. A family F of sets is (p,q)-Helly when every (p,q)-intersecting subfamily F' ⊆ F has total intersection of cardinality at least q. A graph G is a (p, q)- clique-Helly graph when its family of cliques (maximal complete sets) is (P, q)-Helly. According to this terminology, the usual Helly property and the clique-Helly graphs correspond to the case p = 2, q = 1. In this work we present characterizations for (p,q)-Helly families of sets and (p,q)-clique-Helly graphs. For fixed p,q those characterizations lead to polynomial-time recognition algorithms. When p or q is not fixed, it is shown that the recognition of (p,q)-clique-Helly graphs is NP-hard. We also extend further the notions presented, by defining the (p,q, r)-Helly property (which holds when every (p, q)-intersecting subfamily F' ⊆ F has total intersection of cardinality at least r) and giving a way of recognizing (p, q, r)-Helly families in terms of the (p, q)-Helly property. |
publishDate |
2002 |
dc.date.issued.fl_str_mv |
2002-12-31 |
dc.date.accessioned.fl_str_mv |
2017-05-12T14:03:31Z |
dc.date.available.fl_str_mv |
2023-11-30T03:00:28Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/report |
format |
report |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
DOURADO, M. C. ; PROTTI, F. ; SZWARCFITER, J. L.A generalization of the helly property applied to the cliques of a graph. Rio de Janeiro: NCE, UFRJ, 2002. 25 p. (Relatório Técnico, 01/02) |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/11422/1985 |
identifier_str_mv |
DOURADO, M. C. ; PROTTI, F. ; SZWARCFITER, J. L.A generalization of the helly property applied to the cliques of a graph. Rio de Janeiro: NCE, UFRJ, 2002. 25 p. (Relatório Técnico, 01/02) |
url |
http://hdl.handle.net/11422/1985 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Relatório Técnico NCE |
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info:eu-repo/semantics/openAccess |
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openAccess |
dc.publisher.country.fl_str_mv |
Brasil |
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Instituto Tércio Pacitti de Aplicações e Pesquisas Computacionais |
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UFRJ |
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