Coloração acíclica
| Ano de defesa: | 2019 |
|---|---|
| Autor(a) principal: | |
| Orientador(a): | |
| Banca de defesa: | |
| Tipo de documento: | Dissertação |
| Tipo de acesso: | Acesso aberto |
| Idioma: | por |
| Instituição de defesa: |
Não Informado pela instituição
|
| Programa de Pós-Graduação: |
Não Informado pela instituição
|
| Departamento: |
Não Informado pela instituição
|
| País: |
Não Informado pela instituição
|
| Palavras-chave em Português: | |
| Link de acesso: | http://www.repositorio.ufc.br/handle/riufc/40994 |
Resumo: | We will present the state of the art for a sub-area of coloration in graphs known as acyclic coloration. Given a G fi nite graph, we have an acyclic k-coloration of G when we have a proper k-coloration for G such that any two color classes induce in G a vector, that is, an acyclic subgraph. The smallest positive integer k such that G admits an acyclic k-coloration is the acyclic chromatic number of G, denoted by χa (G). We believe that this is the first text to summarize the state of the art for this problem, even considering other languages. We present the results organized by type. First, we present those related to the limitation for the acyclic chromatic number, referring to the cyclic coloration in vertices, in edges and acyclic coloration by lists in vertices and edges. Next, we list the results concerning the computational complexity of the problem of determining if it is possible to acyclically colorize a graph G with k colors, given a graph G and a positive integer k. Finally, we present open questions for future research. |
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Medeiros, Pedro Paulo deAraújo, Júlio César Silva2019-04-23T18:13:37Z2019-04-23T18:13:37Z2019MEDEIROS, Pedro Paulo de. Coloração acíclica. 2019. 65 f. Dissertação (Mestrado Acadêmico em Matemática) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2019.http://www.repositorio.ufc.br/handle/riufc/40994We will present the state of the art for a sub-area of coloration in graphs known as acyclic coloration. Given a G fi nite graph, we have an acyclic k-coloration of G when we have a proper k-coloration for G such that any two color classes induce in G a vector, that is, an acyclic subgraph. The smallest positive integer k such that G admits an acyclic k-coloration is the acyclic chromatic number of G, denoted by χa (G). We believe that this is the first text to summarize the state of the art for this problem, even considering other languages. We present the results organized by type. First, we present those related to the limitation for the acyclic chromatic number, referring to the cyclic coloration in vertices, in edges and acyclic coloration by lists in vertices and edges. Next, we list the results concerning the computational complexity of the problem of determining if it is possible to acyclically colorize a graph G with k colors, given a graph G and a positive integer k. Finally, we present open questions for future research.Apresentaremos o estado da arte para uma subárea de coloração em grafos conhecida como coloração acíclica. Dado um grafo G finito, temos uma k-coloração acíclica de G quando temos uma k-coloração própria para G tal que quaisquer duas classes de cor induzem em G uma floresta, ou seja, um subgrafo acíclico. O menor inteiro positivo k tal que G admite uma k-coloração acíclica é o número cromático acíclico de G, denotado por χa(G). Acreditamos que este seja o primeiro texto a resumir o estado da arte para este problema, mesmo considerando outras línguas. Apresentamos os resultados organizados por tipo. Primeiro, apresentamos aqueles relativos à limitantes para o número cromático acíclico, referentes à coloração cíclica em vértices, em arestas e coloração acíclica por listas em vértices e arestas. Em seguida, listamos os resultados referentes à complexidade computacional do problema de determinar se é possível colorir aciclicamente um grafo G com k cores, dados um grafo G e um inteiro positivo k. Por fim, apresentamos problemas em aberto para a pesquisa futura.Análise combinatóriaTeoria dos grafosColoração de grafosColoração acíclicaCombinatorial analysisTheory of graphsColor in graphsAcyclic stainingColoração acíclicaAcyclic coloringinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessORIGINAL2019_dis_ppmedeiros.pdf2019_dis_ppmedeiros.pdfDissertaçao de Pedro Pauloapplication/pdf1208035http://repositorio.ufc.br/bitstream/riufc/40994/3/2019_dis_ppmedeiros.pdf513756a73922afa86a843f30facde325MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-81748http://repositorio.ufc.br/bitstream/riufc/40994/4/license.txt8a4605be74aa9ea9d79846c1fba20a33MD54riufc/409942019-08-16 14:50:10.497oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2019-08-16T17:50:10Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false |
| dc.title.pt_BR.fl_str_mv |
Coloração acíclica |
| dc.title.en.pt_BR.fl_str_mv |
Acyclic coloring |
| title |
Coloração acíclica |
| spellingShingle |
Coloração acíclica Medeiros, Pedro Paulo de Análise combinatória Teoria dos grafos Coloração de grafos Coloração acíclica Combinatorial analysis Theory of graphs Color in graphs Acyclic staining |
| title_short |
Coloração acíclica |
| title_full |
Coloração acíclica |
| title_fullStr |
Coloração acíclica |
| title_full_unstemmed |
Coloração acíclica |
| title_sort |
Coloração acíclica |
| author |
Medeiros, Pedro Paulo de |
| author_facet |
Medeiros, Pedro Paulo de |
| author_role |
author |
| dc.contributor.author.fl_str_mv |
Medeiros, Pedro Paulo de |
| dc.contributor.advisor1.fl_str_mv |
Araújo, Júlio César Silva |
| contributor_str_mv |
Araújo, Júlio César Silva |
| dc.subject.por.fl_str_mv |
Análise combinatória Teoria dos grafos Coloração de grafos Coloração acíclica Combinatorial analysis Theory of graphs Color in graphs Acyclic staining |
| topic |
Análise combinatória Teoria dos grafos Coloração de grafos Coloração acíclica Combinatorial analysis Theory of graphs Color in graphs Acyclic staining |
| description |
We will present the state of the art for a sub-area of coloration in graphs known as acyclic coloration. Given a G fi nite graph, we have an acyclic k-coloration of G when we have a proper k-coloration for G such that any two color classes induce in G a vector, that is, an acyclic subgraph. The smallest positive integer k such that G admits an acyclic k-coloration is the acyclic chromatic number of G, denoted by χa (G). We believe that this is the first text to summarize the state of the art for this problem, even considering other languages. We present the results organized by type. First, we present those related to the limitation for the acyclic chromatic number, referring to the cyclic coloration in vertices, in edges and acyclic coloration by lists in vertices and edges. Next, we list the results concerning the computational complexity of the problem of determining if it is possible to acyclically colorize a graph G with k colors, given a graph G and a positive integer k. Finally, we present open questions for future research. |
| publishDate |
2019 |
| dc.date.accessioned.fl_str_mv |
2019-04-23T18:13:37Z |
| dc.date.available.fl_str_mv |
2019-04-23T18:13:37Z |
| dc.date.issued.fl_str_mv |
2019 |
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info:eu-repo/semantics/publishedVersion |
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info:eu-repo/semantics/masterThesis |
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masterThesis |
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publishedVersion |
| dc.identifier.citation.fl_str_mv |
MEDEIROS, Pedro Paulo de. Coloração acíclica. 2019. 65 f. Dissertação (Mestrado Acadêmico em Matemática) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2019. |
| dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufc.br/handle/riufc/40994 |
| identifier_str_mv |
MEDEIROS, Pedro Paulo de. Coloração acíclica. 2019. 65 f. Dissertação (Mestrado Acadêmico em Matemática) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2019. |
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por |
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