Ramsey(3,3) = 6

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.contributorUniversidade Estadual Paulista (UNESP)-
Autor(es): dc.creatorPegg Jr, Ed-
Data de aceite: dc.date.accessioned2019-08-21T18:14:46Z-
Data de disponibilização: dc.date.available2019-08-21T18:14:46Z-
Data de envio: dc.date.issued2016-10-26-
Data de envio: dc.date.issued2016-10-26-
Fonte completa do material: dc.identifierhttp://acervodigital.unesp.br/handle/unesp/360897-
Fonte completa do material: dc.identifierhttp://objetoseducacionais2.mec.gov.br/handle/mec/6083-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/467103-
Descrição: dc.descriptionnone-
Descrição: dc.descriptionThe game of Sim, invented by Gustavus Simmons, matches Red against Blue on a hexagonal field of six dots. The players take turns drawing a line of their respective color between pairs of unconnected dots, losing if they make a triangle of their own color first. This Demonstration shows all the 32768 2-colorings of the hexagon. When a set of vertices makes a triangle, the vertices are circled. All of the colorings contain at least one triangle. The Ramsey problem R?(a,a) asks for the smallest n so that the complete graph Kn always contains a smaller monochromatic subgraph Ka, no matter how Kn is 2-colored. The graph that connects three points, K3, is a triangle. Since K5 can be 2-colored with no triangles (red star, blue pentagon), and since k6 always contains a triangle, the solution to the Ramsey problem R(3,3) is 6. The solution for R(4,4) is 18, with the 17-Paley graph and its inverse providing a 2-coloring for K17 without K4. The solution for R(5,5) is currently unknown, and it is predicted that the solution to R(6,6) will never be known-
Descrição: dc.descriptionComponente Curricular::Ensino Fundamental::Séries Finais::Matemática-
Relação: dc.relation131Ramsey336.nbp-
Direitos: dc.rightsDemonstration freeware using Mathematica Player-
Palavras-chave: dc.subjectCombinatorics-
Palavras-chave: dc.subjectGraph Theory-
Palavras-chave: dc.subjectUnsolved Problems-
Palavras-chave: dc.subjectEducação Básica::Ensino Fundamental Final::Matemática::Espaço e forma-
Título: dc.titleRamsey(3,3) = 6-
Tipo de arquivo: dc.typetexto-
Aparece nas coleções:Repositório Institucional - Acervo Digital Unesp

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