Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Ramseys_theorem> ?p ?o }
- Ramseys_theorem abstract "In combinatorics, Ramsey's theorem states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To demonstrate the theorem for two colours (say, blue and red), let r and s be any two positive integers. Ramsey's theorem states that there exists a least positive integer R(r, s) for which every blue-red edge colouring of the complete graph on R(r, s) vertices contains a blue clique on r vertices or a red clique on s vertices. (Here R(r, s) signifies an integer that depends on both r and s.)Ramsey's theorem is a foundational result in combinatorics. The first version of this result was proved by F. P. Ramsey. This initiated the combinatorial theory now called Ramsey theory, that seeks regularity amid disorder: general conditions for the existence of substructures with regular properties. In this application it is a question of the existence of monochromatic subsets, that is, subsets of connected edges of just one colour.An extension of this theorem applies to any finite number of colours, rather than just two. More precisely, the theorem states that for any given number of colours, c, and any given integers n1, …, nc, there is a number, R(n1, …, nc), such that if the edges of a complete graph of order R(n1, ..., nc) are coloured with c different colours, then for some i between 1 and c, it must contain a complete subgraph of order ni whose edges are all colour i. The special case above has c = 2 (and n1 = r and n2 = s).".
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- Ramseys_theorem wikiPageWikiLink Clebsch_graph.
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- Ramseys_theorem wikiPageWikiLinkText "Ramsey number".
- Ramseys_theorem wikiPageWikiLinkText "Ramsey numbers".
- Ramseys_theorem wikiPageWikiLinkText "Ramsey".
- Ramseys_theorem wikiPageWikiLinkText "Ramsey's Theorem".
- Ramseys_theorem wikiPageWikiLinkText "Ramsey's theorem".
- Ramseys_theorem wikiPageWikiLinkText "Ramsey's theorem#Ramsey numbers".
- Ramseys_theorem wikiPageWikiLinkText "finite Ramsey theorem".
- Ramseys_theorem wikiPageWikiLinkText "infinite Ramsey theorem".
- Ramseys_theorem id "p/r077240".
- Ramseys_theorem title "Ramsey theorem".
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- Ramseys_theorem subject Category:Articles_containing_proofs.
- Ramseys_theorem subject Category:Ramsey_theory.
- Ramseys_theorem subject Category:Theorems_in_graph_theory.
- Ramseys_theorem type Combinatoric.
- Ramseys_theorem type Proof.
- Ramseys_theorem type Redirect.
- Ramseys_theorem type Theorem.
- Ramseys_theorem comment "In combinatorics, Ramsey's theorem states that one will find monochromatic cliques in any edge labelling (with colours) of a sufficiently large complete graph. To demonstrate the theorem for two colours (say, blue and red), let r and s be any two positive integers. Ramsey's theorem states that there exists a least positive integer R(r, s) for which every blue-red edge colouring of the complete graph on R(r, s) vertices contains a blue clique on r vertices or a red clique on s vertices.".
- Ramseys_theorem label "Ramsey's theorem".
- Ramseys_theorem sameAs Q918099.
- Ramseys_theorem sameAs مبرهنة_رامزي.
- Ramseys_theorem sameAs Satz_von_Ramsey.
- Ramseys_theorem sameAs Θεώρημα_Ράμσεϋ.