Coloração de Arestas em Grafos Split-Comparabilidade
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/9140 |
Resumo: | Let G = (V, E) be a simple and undirected graph. An edge-coloring is an assignment of colors to the edges of the graph such that any two adjacent edges receive different colors. The chromatic index of a graph G is the smallest number of colors such that G has an edge-coloring. Clearly, a lower bound for the chromatic index is the degree of the vertex of higher degree, denoted by ?(G). In 1964, Vizing proved that chromatic index is ?(G) or ?(G) + 1. The Classification Problem is to determine if the chromatic index is ?(G) (Class 1 ) or if it is ?(G) + 1 (Class 2 ). Let n be number of vertices of a graph G and let m be its number of edges. We say G is overfull if m > (n-1) 2 ?(G). Every overfull graph is Class 2. A graph is subgraph-overfull if it has a subgraph with same maximum degree and it is overfull. It is well-known that every overfull and subgraph-overfull graph is Class 2. The Overfull Conjecture asserts that every graph with ?(G) > n 3 is Class 2 if and only if it is subgraph-overfull. In this work we prove the Overfull Conjecture to a particular class of graphs, known as split-comparability graphs. The Overfull Conjecture was open to this class. |
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Cruz, Jadder Bismarck de SousaSilva, Cândida Nunes dahttp://lattes.cnpq.br/6019111128413167Almeida, Sheila Morais dehttp://lattes.cnpq.br/9151881548763857http://lattes.cnpq.br/2157434731256503ffd0da4e-26e1-439a-8c78-569dc85f42b62017-10-09T16:27:11Z2017-10-09T16:27:11Z2017-05-02CRUZ, Jadder Bismarck de Sousa. Coloração de Arestas em Grafos Split-Comparabilidade. 2017. Dissertação (Mestrado em Ciência da Computação) – Universidade Federal de São Carlos, Sorocaba, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9140.https://repositorio.ufscar.br/handle/ufscar/9140Let G = (V, E) be a simple and undirected graph. An edge-coloring is an assignment of colors to the edges of the graph such that any two adjacent edges receive different colors. The chromatic index of a graph G is the smallest number of colors such that G has an edge-coloring. Clearly, a lower bound for the chromatic index is the degree of the vertex of higher degree, denoted by ?(G). In 1964, Vizing proved that chromatic index is ?(G) or ?(G) + 1. The Classification Problem is to determine if the chromatic index is ?(G) (Class 1 ) or if it is ?(G) + 1 (Class 2 ). Let n be number of vertices of a graph G and let m be its number of edges. We say G is overfull if m > (n-1) 2 ?(G). Every overfull graph is Class 2. A graph is subgraph-overfull if it has a subgraph with same maximum degree and it is overfull. It is well-known that every overfull and subgraph-overfull graph is Class 2. The Overfull Conjecture asserts that every graph with ?(G) > n 3 is Class 2 if and only if it is subgraph-overfull. In this work we prove the Overfull Conjecture to a particular class of graphs, known as split-comparability graphs. The Overfull Conjecture was open to this class.Dado um grafo simples e não direcionado G = (V, E), uma coloração de arestas é uma função que atribui cores às arestas do grafo tal que todas as arestas que incidem em um mesmo vértice têm cores distintas. O índice cromático é o número mínimo de cores para obter uma coloração própria das arestas de um grafo. Um limite inferior para o índice cromático é, claramente, o grau do vértice de maior grau, denotado por ?(G). Em 1964, Vizing provou que o índice cromático ou é ?(G) ou ?(G) + 1, surgindo assim o Problema da Classificação, que consiste em determinar se o índice cromático é ?(G) (Classe 1 ) ou ?(G) + 1 (Classe 2 ). Seja n o número de vértices de um grafo G e m seu número de arestas. Dizemos que um grafo é sobrecarregado se m > (n-1) 2 ?(G). Um grafo é subgrafo-sobrecarregado se tem um subgrafo de mesmo grau máximo que é sobrecarregado. É sabido que se um grafo é sobrecarregado ou subgrafo-sobrecarregado ele é necessariamente Classe 2. A Conjectura Overfull é uma famosa conjectura de coloração de arestas e diz que um grafo com ?(G) > n 3 é Classe 2 se e somente se é subgrafo-sobrecarregado. Neste trabalho provamos a Conjectura Overfull para uma classe de grafos, a classe dos grafos split-comparabilidade. Até este momento a Conjectura Overfull estava aberta para esta classe.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus SorocabaPrograma de Pós-Graduação em Ciência da Computação - PPGCC-SoUFSCarTeoria dos grafosColoração de arestasProblema da ClassificaçãoGrafos comparabilidadeClassification ProblemGraph theoryGrafos splitEdge coloringChromatic indexSplit graphsComparability graphsCIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAOColoração de Arestas em Grafos Split-ComparabilidadeEdge coloring in split-comparability graphsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnline600600ec71de3c-0edf-486d-aa7d-8bb67d716b9ainfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALCRUZ_Jadder_2017.pdfCRUZ_Jadder_2017.pdfapplication/pdf1326879https://repositorio.ufscar.br/bitstream/ufscar/9140/1/CRUZ_Jadder_2017.pdf61ee3c40e293d26085a939c0a0290716MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/9140/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTCRUZ_Jadder_2017.pdf.txtCRUZ_Jadder_2017.pdf.txtExtracted texttext/plain80294https://repositorio.ufscar.br/bitstream/ufscar/9140/3/CRUZ_Jadder_2017.pdf.txtd3b97affcff6cc7025a736781bc0a46bMD53THUMBNAILCRUZ_Jadder_2017.pdf.jpgCRUZ_Jadder_2017.pdf.jpgIM Thumbnailimage/jpeg5191https://repositorio.ufscar.br/bitstream/ufscar/9140/4/CRUZ_Jadder_2017.pdf.jpg56312bcd14aa9a5d5ed6c118d655c4f6MD54ufscar/91402023-09-18 18:31:26.567oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:26Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Coloração de Arestas em Grafos Split-Comparabilidade |
dc.title.alternative.eng.fl_str_mv |
Edge coloring in split-comparability graphs |
title |
Coloração de Arestas em Grafos Split-Comparabilidade |
spellingShingle |
Coloração de Arestas em Grafos Split-Comparabilidade Cruz, Jadder Bismarck de Sousa Teoria dos grafos Coloração de arestas Problema da Classificação Grafos comparabilidade Classification Problem Graph theory Grafos split Edge coloring Chromatic index Split graphs Comparability graphs CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
title_short |
Coloração de Arestas em Grafos Split-Comparabilidade |
title_full |
Coloração de Arestas em Grafos Split-Comparabilidade |
title_fullStr |
Coloração de Arestas em Grafos Split-Comparabilidade |
title_full_unstemmed |
Coloração de Arestas em Grafos Split-Comparabilidade |
title_sort |
Coloração de Arestas em Grafos Split-Comparabilidade |
author |
Cruz, Jadder Bismarck de Sousa |
author_facet |
Cruz, Jadder Bismarck de Sousa |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/2157434731256503 |
dc.contributor.author.fl_str_mv |
Cruz, Jadder Bismarck de Sousa |
dc.contributor.advisor1.fl_str_mv |
Silva, Cândida Nunes da |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/6019111128413167 |
dc.contributor.advisor-co1.fl_str_mv |
Almeida, Sheila Morais de |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/9151881548763857 |
dc.contributor.authorID.fl_str_mv |
ffd0da4e-26e1-439a-8c78-569dc85f42b6 |
contributor_str_mv |
Silva, Cândida Nunes da Almeida, Sheila Morais de |
dc.subject.por.fl_str_mv |
Teoria dos grafos Coloração de arestas Problema da Classificação Grafos comparabilidade Classification Problem |
topic |
Teoria dos grafos Coloração de arestas Problema da Classificação Grafos comparabilidade Classification Problem Graph theory Grafos split Edge coloring Chromatic index Split graphs Comparability graphs CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
dc.subject.eng.fl_str_mv |
Graph theory Grafos split Edge coloring Chromatic index Split graphs Comparability graphs |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO |
description |
Let G = (V, E) be a simple and undirected graph. An edge-coloring is an assignment of colors to the edges of the graph such that any two adjacent edges receive different colors. The chromatic index of a graph G is the smallest number of colors such that G has an edge-coloring. Clearly, a lower bound for the chromatic index is the degree of the vertex of higher degree, denoted by ?(G). In 1964, Vizing proved that chromatic index is ?(G) or ?(G) + 1. The Classification Problem is to determine if the chromatic index is ?(G) (Class 1 ) or if it is ?(G) + 1 (Class 2 ). Let n be number of vertices of a graph G and let m be its number of edges. We say G is overfull if m > (n-1) 2 ?(G). Every overfull graph is Class 2. A graph is subgraph-overfull if it has a subgraph with same maximum degree and it is overfull. It is well-known that every overfull and subgraph-overfull graph is Class 2. The Overfull Conjecture asserts that every graph with ?(G) > n 3 is Class 2 if and only if it is subgraph-overfull. In this work we prove the Overfull Conjecture to a particular class of graphs, known as split-comparability graphs. The Overfull Conjecture was open to this class. |
publishDate |
2017 |
dc.date.accessioned.fl_str_mv |
2017-10-09T16:27:11Z |
dc.date.available.fl_str_mv |
2017-10-09T16:27:11Z |
dc.date.issued.fl_str_mv |
2017-05-02 |
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 |
CRUZ, Jadder Bismarck de Sousa. Coloração de Arestas em Grafos Split-Comparabilidade. 2017. Dissertação (Mestrado em Ciência da Computação) – Universidade Federal de São Carlos, Sorocaba, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9140. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/9140 |
identifier_str_mv |
CRUZ, Jadder Bismarck de Sousa. Coloração de Arestas em Grafos Split-Comparabilidade. 2017. Dissertação (Mestrado em Ciência da Computação) – Universidade Federal de São Carlos, Sorocaba, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9140. |
url |
https://repositorio.ufscar.br/handle/ufscar/9140 |
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por |
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por |
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600 600 |
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ec71de3c-0edf-486d-aa7d-8bb67d716b9a |
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info:eu-repo/semantics/openAccess |
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openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus Sorocaba |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Ciência da Computação - PPGCC-So |
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UFSCar |
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Universidade Federal de São Carlos Câmpus Sorocaba |
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