Planaridade em grafos: o teorema de Kuratowski

Detalhes bibliográficos
Autor(a) principal: Santos, Emanoel Lázaro de Santana
Data de Publicação: 2017
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFS
Texto Completo: https://ri.ufs.br/handle/riufs/7018
Resumo: The present dissertation aims to introduce the basic concepts of graph theory to explore the concept of planarity and present a beautiful theorem connected to this theme. Graph theory is a very effective tool for solving problems involving several areas of knowledge. Some of these problems are related to planarity of graphs. Thus, this work presents Kuratowski’s theorem, with the beauty of its demonstration, which provides a necessary and sufficient condition for a graph to be planar, observing if it contains a specific type of subgraph related to complete and split graphs.
id UFS-2_913af3002bae5e60e097108a6e4d86ee
oai_identifier_str oai:ufs.br:riufs/7018
network_acronym_str UFS-2
network_name_str Repositório Institucional da UFS
repository_id_str
spelling Santos, Emanoel Lázaro de SantanaGouveia, Giovana Siracusa2017-11-28T21:19:45Z2017-11-28T21:19:45Z2017-08-26SANTOS, Emanoel Lázaro de Santana. Planaridade em grafos : o teorema de Kuratowski. 2017. 84 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, SE, 2017.https://ri.ufs.br/handle/riufs/7018The present dissertation aims to introduce the basic concepts of graph theory to explore the concept of planarity and present a beautiful theorem connected to this theme. Graph theory is a very effective tool for solving problems involving several areas of knowledge. Some of these problems are related to planarity of graphs. Thus, this work presents Kuratowski’s theorem, with the beauty of its demonstration, which provides a necessary and sufficient condition for a graph to be planar, observing if it contains a specific type of subgraph related to complete and split graphs.A presente dissertaçãoo tem como objetivo introduzir os conceitos básicos da teoria dos grafos para explorar o conceito de planaridade e apresentar um belo teorema ligado a esse tema. A teoria dos grafos é uma ferramenta muito eficaz na resolução de problemas que envolvem diversas áreas de conhecimento. Alguns destes problemas estão relacionados `a planaridade de grafos. Dessa forma, este trabalho apresenta o teorema de Kuratowski, com a beleza de sua demonstra¸c˜ao, que fornece uma condição necessária e suficiente para um grafo ser planar, observando se o mesmo contém um tipo específico de subgrafo relacionado a grafos completos e bipartidos.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão Cristóvão, SEporMatemáticaTeoria dos grafosGrafo planarTeorema de KuratowskiTheory of graphsPlanar graphKuratowski’s theoremCIENCIAS EXATAS E DA TERRA::MATEMATICAPlanaridade em grafos: o teorema de KuratowskiPlanarity in graphs : Kuratowski’s theoreminfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisMestrado Profissional em MatemáticaUniversidade Federal de Sergipereponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/7018/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALEMANOEL_LAZARO_SANTANA_SANTOS.pdfEMANOEL_LAZARO_SANTANA_SANTOS.pdfapplication/pdf2012986https://ri.ufs.br/jspui/bitstream/riufs/7018/2/EMANOEL_LAZARO_SANTANA_SANTOS.pdfe24fac237d4de6f9847d04f00096747fMD52TEXTEMANOEL_LAZARO_SANTANA_SANTOS.pdf.txtEMANOEL_LAZARO_SANTANA_SANTOS.pdf.txtExtracted texttext/plain123402https://ri.ufs.br/jspui/bitstream/riufs/7018/3/EMANOEL_LAZARO_SANTANA_SANTOS.pdf.txt36a4edaac9a9a1973e4b7d0a6217df89MD53THUMBNAILEMANOEL_LAZARO_SANTANA_SANTOS.pdf.jpgEMANOEL_LAZARO_SANTANA_SANTOS.pdf.jpgGenerated Thumbnailimage/jpeg1182https://ri.ufs.br/jspui/bitstream/riufs/7018/4/EMANOEL_LAZARO_SANTANA_SANTOS.pdf.jpg08750a1884182646395510f80df28640MD54riufs/70182017-11-29 18:32:28.389oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2017-11-29T21:32:28Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv Planaridade em grafos: o teorema de Kuratowski
dc.title.alternative.eng.fl_str_mv Planarity in graphs : Kuratowski’s theorem
title Planaridade em grafos: o teorema de Kuratowski
spellingShingle Planaridade em grafos: o teorema de Kuratowski
Santos, Emanoel Lázaro de Santana
Matemática
Teoria dos grafos
Grafo planar
Teorema de Kuratowski
Theory of graphs
Planar graph
Kuratowski’s theorem
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Planaridade em grafos: o teorema de Kuratowski
title_full Planaridade em grafos: o teorema de Kuratowski
title_fullStr Planaridade em grafos: o teorema de Kuratowski
title_full_unstemmed Planaridade em grafos: o teorema de Kuratowski
title_sort Planaridade em grafos: o teorema de Kuratowski
author Santos, Emanoel Lázaro de Santana
author_facet Santos, Emanoel Lázaro de Santana
author_role author
dc.contributor.author.fl_str_mv Santos, Emanoel Lázaro de Santana
dc.contributor.advisor1.fl_str_mv Gouveia, Giovana Siracusa
contributor_str_mv Gouveia, Giovana Siracusa
dc.subject.por.fl_str_mv Matemática
Teoria dos grafos
Grafo planar
Teorema de Kuratowski
Theory of graphs
Planar graph
Kuratowski’s theorem
topic Matemática
Teoria dos grafos
Grafo planar
Teorema de Kuratowski
Theory of graphs
Planar graph
Kuratowski’s theorem
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description The present dissertation aims to introduce the basic concepts of graph theory to explore the concept of planarity and present a beautiful theorem connected to this theme. Graph theory is a very effective tool for solving problems involving several areas of knowledge. Some of these problems are related to planarity of graphs. Thus, this work presents Kuratowski’s theorem, with the beauty of its demonstration, which provides a necessary and sufficient condition for a graph to be planar, observing if it contains a specific type of subgraph related to complete and split graphs.
publishDate 2017
dc.date.accessioned.fl_str_mv 2017-11-28T21:19:45Z
dc.date.available.fl_str_mv 2017-11-28T21:19:45Z
dc.date.issued.fl_str_mv 2017-08-26
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv SANTOS, Emanoel Lázaro de Santana. Planaridade em grafos : o teorema de Kuratowski. 2017. 84 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, SE, 2017.
dc.identifier.uri.fl_str_mv https://ri.ufs.br/handle/riufs/7018
identifier_str_mv SANTOS, Emanoel Lázaro de Santana. Planaridade em grafos : o teorema de Kuratowski. 2017. 84 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, SE, 2017.
url https://ri.ufs.br/handle/riufs/7018
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.program.fl_str_mv Mestrado Profissional em Matemática
dc.publisher.initials.fl_str_mv Universidade Federal de Sergipe
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFS
instname:Universidade Federal de Sergipe (UFS)
instacron:UFS
instname_str Universidade Federal de Sergipe (UFS)
instacron_str UFS
institution UFS
reponame_str Repositório Institucional da UFS
collection Repositório Institucional da UFS
bitstream.url.fl_str_mv https://ri.ufs.br/jspui/bitstream/riufs/7018/1/license.txt
https://ri.ufs.br/jspui/bitstream/riufs/7018/2/EMANOEL_LAZARO_SANTANA_SANTOS.pdf
https://ri.ufs.br/jspui/bitstream/riufs/7018/3/EMANOEL_LAZARO_SANTANA_SANTOS.pdf.txt
https://ri.ufs.br/jspui/bitstream/riufs/7018/4/EMANOEL_LAZARO_SANTANA_SANTOS.pdf.jpg
bitstream.checksum.fl_str_mv 098cbbf65c2c15e1fb2e49c5d306a44c
e24fac237d4de6f9847d04f00096747f
36a4edaac9a9a1973e4b7d0a6217df89
08750a1884182646395510f80df28640
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)
repository.mail.fl_str_mv repositorio@academico.ufs.br
_version_ 1802110808757370880

Registros relacionados