Edge clique graphs and some classes of chordal graphs
Autor(a) principal: | |
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Data de Publicação: | 1999 |
Outros Autores: | |
Tipo de documento: | Relatório |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRJ |
Texto Completo: | http://hdl.handle.net/11422/2658 |
Resumo: | The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. This class of graphs has been introduced by Albertson and Collins (1984). Although many interesting properties of it have been since studied, we do not know complete characterizations of edge clique graphs of any non trivial class of graphs. In this paper, we describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlikethreshold, split and threshold graphs. In special, a known necessary condition for a graph to be an edge clique graph is that the sizes of all maximal cliques and intersections of ma.ximal cliques ought to be triangular numbers. We show that this condition is also suflicient for starlike-threshold graphs. |
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Cerioli, Márcia RosanaSzwarcfiter, Jayme Luiz2017-08-15T14:09:39Z2023-11-30T03:00:27Z1999-12-31CERIOLI, M. R; SZWARCFITER, J. L. Edge clique graphs and some classes of chordal graphs. Rio de Janeiro: NCE, UFRJ, 1999. 17 p. (Relatório Técnico, 21/99)http://hdl.handle.net/11422/2658The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. This class of graphs has been introduced by Albertson and Collins (1984). Although many interesting properties of it have been since studied, we do not know complete characterizations of edge clique graphs of any non trivial class of graphs. In this paper, we describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlikethreshold, split and threshold graphs. In special, a known necessary condition for a graph to be an edge clique graph is that the sizes of all maximal cliques and intersections of ma.ximal cliques ought to be triangular numbers. We show that this condition is also suflicient for starlike-threshold graphs.Submitted by Elaine Almeida (elaine.almeida@nce.ufrj.br) on 2017-08-15T14:09:39Z No. of bitstreams: 1 21_99_000611340.pdf: 819412 bytes, checksum: 220c7f83a02980cfbb728054af4eac87 (MD5)Made available in DSpace on 2017-08-15T14:09:39Z (GMT). No. of bitstreams: 1 21_99_000611340.pdf: 819412 bytes, checksum: 220c7f83a02980cfbb728054af4eac87 (MD5) Previous issue date: 1999-12-31engRelatório Técnico NCECNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAOGrafos cordalMargens de grafos cliqueChordal graphsEdge clique graphssplit graphsEdge clique graphs and some classes of chordal graphsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/report2199abertoBrasilInstituto Tércio Pacitti de Aplicações e Pesquisas Computacionaisinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRJinstname:Universidade Federal do Rio de Janeiro (UFRJ)instacron:UFRJORIGINAL21_99_000611340.pdf21_99_000611340.pdfapplication/pdf819412http://pantheon.ufrj.br:80/bitstream/11422/2658/1/21_99_000611340.pdf220c7f83a02980cfbb728054af4eac87MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81853http://pantheon.ufrj.br:80/bitstream/11422/2658/2/license.txtdd32849f2bfb22da963c3aac6e26e255MD52TEXT21_99_000611340.pdf.txt21_99_000611340.pdf.txtExtracted texttext/plain31183http://pantheon.ufrj.br:80/bitstream/11422/2658/3/21_99_000611340.pdf.txtcc34cf4b4fbf2707bfd62a3ff35c3dafMD5311422/26582023-11-30 00:00:27.087oai:pantheon.ufrj.br:11422/2658TElDRU7Dh0EgTsODTy1FWENMVVNJVkEgREUgRElTVFJJQlVJw4fDg08KCkFvIGFzc2luYXIgZSBlbnRyZWdhciBlc3RhIGxpY2Vuw6dhLCB2b2PDqihzKSBvKHMpIGF1dG9yKGVzKSBvdSBwcm9wcmlldMOhcmlvKHMpIGRvcyBkaXJlaXRvcyBhdXRvcmFpcyBjb25jZWRlKG0pIGFvIFJlcG9zaXTDs3JpbyBQYW50aGVvbiBkYSBVbml2ZXJzaWRhZGUgRmVkZXJhbCBkbyBSaW8gZGUgSmFuZWlybyAoVUZSSikgbyBkaXJlaXRvIG7Do28gLSBleGNsdXNpdm8gZGUgcmVwcm9kdXppciwgY29udmVydGVyIChjb21vIGRlZmluaWRvIGFiYWl4byksIGUvb3UgZGlzdHJpYnVpciBvIGRvY3VtZW50byBlbnRyZWd1ZSAoaW5jbHVpbmRvIG8gcmVzdW1vKSBlbSB0b2RvIG8gbXVuZG8sIGVtIGZvcm1hdG8gZWxldHLDtG5pY28gZSBlbSBxdWFscXVlciBtZWlvLCBpbmNsdWluZG8sIG1hcyBuw6NvIGxpbWl0YWRvIGEgw6F1ZGlvIGUvb3UgdsOtZGVvLgoKVm9jw6ogY29uY29yZGEgcXVlIGEgVUZSSiBwb2RlLCBzZW0gYWx0ZXJhciBvIGNvbnRlw7pkbywgdHJhZHV6aXIgYSBhcHJlc2VudGHDp8OjbyBkZSBxdWFscXVlciBtZWlvIG91IGZvcm1hdG8gY29tIGEgZmluYWxpZGFkZSBkZSBwcmVzZXJ2YcOnw6NvLgoKVm9jw6ogdGFtYsOpbSBjb25jb3JkYSBxdWUgYSBVRlJKIHBvZGUgbWFudGVyIG1haXMgZGUgdW1hIGPDs3BpYSBkZXNzYSBzdWJtaXNzw6NvIHBhcmEgZmlucyBkZSBzZWd1cmFuw6dhLCBiYWNrLXVwIGUgcHJlc2VydmHDp8OjbyBkaWdpdGFsLgoKRGVjbGFyYSBxdWUgbyBkb2N1bWVudG8gZW50cmVndWUgw6kgc2V1IHRyYWJhbGhvIG9yaWdpbmFsLCBlIHF1ZSB2b2PDqiB0ZW0gbyBkaXJlaXRvIGRlIGNvbmNlZGVyIG9zIGRpcmVpdG9zIGNvbnRpZG9zIG5lc3RhIGxpY2Vuw6dhLiBWb2PDqiB0YW1iw6ltIGRlY2xhcmEgcXVlIGEgc3VhIGFwcmVzZW50YcOnw6NvLCBjb20gbyBtZWxob3IgZGUgc2V1cyBjb25oZWNpbWVudG9zLCBuw6NvIGluZnJpbmdpIGRpcmVpdG9zIGF1dG9yYWlzIGRlIHRlcmNlaXJvcy4KClNlIG8gZG9jdW1lbnRvIGVudHJlZ3VlIGNvbnTDqW0gbWF0ZXJpYWwgZG8gcXVhbCB2b2PDqiBuw6NvIHRlbSBkaXJlaXRvcyBkZSBhdXRvciwgZGVjbGFyYSBxdWUgb2J0ZXZlIGEgcGVybWlzc8OjbyBpcnJlc3RyaXRhIGRvIGRldGVudG9yIGRvcyBkaXJlaXRvcyBhdXRvcmFpcyBlIGNvbmNlZGUgYSBVRlJKIG9zIGRpcmVpdG9zIHJlcXVlcmlkb3MgcG9yIGVzdGEgbGljZW7Dp2EsIGUgcXVlIGVzc2UgbWF0ZXJpYWwgZGUgcHJvcHJpZWRhZGUgZGUgdGVyY2Vpcm9zIGVzdMOhIGNsYXJhbWVudGUgaWRlbnRpZmljYWRvIGUgcmVjb25oZWNpZG8gbm8gdGV4dG8gb3UgY29udGXDumRvIGRhIHN1Ym1pc3PDo28uCgpTZSBvIGRvY3VtZW50byBlbnRyZWd1ZSDDqSBiYXNlYWRvIGVtIHRyYWJhbGhvIHF1ZSBmb2ksIG91IHRlbSBzaWRvIHBhdHJvY2luYWRvIG91IGFwb2lhZG8gcG9yIHVtYSBhZ8OqbmNpYSBvdSBvdXRybyhzKSBvcmdhbmlzbW8ocykgcXVlIG7Do28gYSBVRlJKLCB2b2PDqiBkZWNsYXJhIHF1ZSBjdW1wcml1IHF1YWxxdWVyIGRpcmVpdG8gZGUgUkVWSVPDg08gb3UgZGUgb3V0cmFzIG9icmlnYcOnw7VlcyByZXF1ZXJpZGFzIHBvciBjb250cmF0byBvdSBhY29yZG8uCgpBIFVGUkogaXLDoSBpZGVudGlmaWNhciBjbGFyYW1lbnRlIG8ocykgc2V1KHMpIG5vbWUocykgY29tbyBhdXRvcihlcykgb3UgcHJvcHJpZXTDoXJpbyhzKSBkYSBzdWJtaXNzw6NvLCBlIG7Do28gZmFyw6EgcXVhbHF1ZXIgYWx0ZXJhw6fDo28sIHBhcmEgYWzDqW0gZGFzIHBlcm1pdGlkYXMgcG9yIGVzdGEgbGljZW7Dp2EsIG5vIGF0byBkZSBzdWJtaXNzw6NvLgo=Repositório de PublicaçõesPUBhttp://www.pantheon.ufrj.br/oai/requestopendoar:2023-11-30T03:00:27Repositório Institucional da UFRJ - Universidade Federal do Rio de Janeiro (UFRJ)false |
dc.title.en.fl_str_mv |
Edge clique graphs and some classes of chordal graphs |
title |
Edge clique graphs and some classes of chordal graphs |
spellingShingle |
Edge clique graphs and some classes of chordal graphs Cerioli, Márcia Rosana CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO Grafos cordal Margens de grafos clique Chordal graphs Edge clique graphs split graphs |
title_short |
Edge clique graphs and some classes of chordal graphs |
title_full |
Edge clique graphs and some classes of chordal graphs |
title_fullStr |
Edge clique graphs and some classes of chordal graphs |
title_full_unstemmed |
Edge clique graphs and some classes of chordal graphs |
title_sort |
Edge clique graphs and some classes of chordal graphs |
author |
Cerioli, Márcia Rosana |
author_facet |
Cerioli, Márcia Rosana Szwarcfiter, Jayme Luiz |
author_role |
author |
author2 |
Szwarcfiter, Jayme Luiz |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Cerioli, Márcia Rosana Szwarcfiter, Jayme Luiz |
dc.subject.cnpq.fl_str_mv |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO |
topic |
CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::TEORIA DA COMPUTACAO Grafos cordal Margens de grafos clique Chordal graphs Edge clique graphs split graphs |
dc.subject.por.fl_str_mv |
Grafos cordal Margens de grafos clique |
dc.subject.eng.fl_str_mv |
Chordal graphs Edge clique graphs split graphs |
description |
The edge clique graph of a graph G is one having as vertices the edges of G, two vertices being adjacent if the corresponding edges of G belong to a common clique. This class of graphs has been introduced by Albertson and Collins (1984). Although many interesting properties of it have been since studied, we do not know complete characterizations of edge clique graphs of any non trivial class of graphs. In this paper, we describe characterizations relative to edge clique graphs and some classes of chordal graphs, such as starlike, starlikethreshold, split and threshold graphs. In special, a known necessary condition for a graph to be an edge clique graph is that the sizes of all maximal cliques and intersections of ma.ximal cliques ought to be triangular numbers. We show that this condition is also suflicient for starlike-threshold graphs. |
publishDate |
1999 |
dc.date.issued.fl_str_mv |
1999-12-31 |
dc.date.accessioned.fl_str_mv |
2017-08-15T14:09:39Z |
dc.date.available.fl_str_mv |
2023-11-30T03:00:27Z |
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 |
CERIOLI, M. R; SZWARCFITER, J. L. Edge clique graphs and some classes of chordal graphs. Rio de Janeiro: NCE, UFRJ, 1999. 17 p. (Relatório Técnico, 21/99) |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/11422/2658 |
identifier_str_mv |
CERIOLI, M. R; SZWARCFITER, J. L. Edge clique graphs and some classes of chordal graphs. Rio de Janeiro: NCE, UFRJ, 1999. 17 p. (Relatório Técnico, 21/99) |
url |
http://hdl.handle.net/11422/2658 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Relatório Técnico NCE |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.country.fl_str_mv |
Brasil |
dc.publisher.department.fl_str_mv |
Instituto Tércio Pacitti de Aplicações e Pesquisas Computacionais |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRJ instname:Universidade Federal do Rio de Janeiro (UFRJ) instacron:UFRJ |
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Universidade Federal do Rio de Janeiro (UFRJ) |
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UFRJ |
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UFRJ |
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