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- Ramsey's_theorem abstract "In combinatorics, Ramsey's theorem states that in any colouring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs. For two colours, Ramsey's theorem states that for any pair of positive integers (r,s), there exists a least positive integer R(r,s) such that for any 2-colouring of the complete graph on R(r,s) vertices, there exists a complete monochromatic subgraph on either r or s vertices. Here R(r,s) signifies an integer that depends on both r and s. It is understood to represent the smallest integer for which the theorem holds.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 oforder 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).".
- Ramsey's_theorem thumbnail RamseyTheory_K5_no_mono_K3.svg?width=300.
- Ramsey's_theorem wikiPageExternalLink PuzzRamsey.html.
- Ramsey's_theorem wikiPageExternalLink index.html.
- Ramsey's_theorem wikiPageExternalLink RamseyNumber.html.
- Ramsey's_theorem wikiPageExternalLink page=48.
- Ramsey's_theorem wikiPageExternalLink sur.pdf.
- Ramsey's_theorem wikiPageExternalLink ramsey-upper-limit.lisp.
- Ramsey's_theorem wikiPageExternalLink ramsey.
- Ramsey's_theorem wikiPageID "184898".
- Ramsey's_theorem wikiPageRevisionID "606336229".
- Ramsey's_theorem hasPhotoCollection Ramsey's_theorem.
- Ramsey's_theorem id "p/r077240".
- Ramsey's_theorem title "Ramsey theorem".
- Ramsey's_theorem subject Category:Articles_containing_proofs.
- Ramsey's_theorem subject Category:Ramsey_theory.
- Ramsey's_theorem subject Category:Theorems_in_graph_theory.
- Ramsey's_theorem type Abstraction100002137.
- Ramsey's_theorem type Communication100033020.
- Ramsey's_theorem type Message106598915.
- Ramsey's_theorem type Proposition106750804.
- Ramsey's_theorem type Statement106722453.
- Ramsey's_theorem type Theorem106752293.
- Ramsey's_theorem type TheoremsInCombinatorics.
- Ramsey's_theorem comment "In combinatorics, Ramsey's theorem states that in any colouring of the edges of a sufficiently large complete graph, one will find monochromatic complete subgraphs. For two colours, Ramsey's theorem states that for any pair of positive integers (r,s), there exists a least positive integer R(r,s) such that for any 2-colouring of the complete graph on R(r,s) vertices, there exists a complete monochromatic subgraph on either r or s vertices.".
- Ramsey's_theorem label "Ramsey's theorem".
- Ramsey's_theorem label "Satz von Ramsey".
- Ramsey's_theorem label "Teorema Finito de Ramsey".
- Ramsey's_theorem label "Teorema de Ramsey".
- Ramsey's_theorem label "Teorema di Ramsey".
- Ramsey's_theorem label "Théorème de Ramsey".
- Ramsey's_theorem label "Twierdzenie Ramseya".
- Ramsey's_theorem label "Теорема Рамсея".
- Ramsey's_theorem label "مبرهنة رمزي".
- Ramsey's_theorem label "ラムゼーの定理".
- Ramsey's_theorem label "拉姆齐定理".
- Ramsey's_theorem sameAs Satz_von_Ramsey.
- Ramsey's_theorem sameAs Θεώρημα_Ράμσεϋ.
- Ramsey's_theorem sameAs Teorema_de_Ramsey.
- Ramsey's_theorem sameAs Théorème_de_Ramsey.
- Ramsey's_theorem sameAs Teorema_di_Ramsey.
- Ramsey's_theorem sameAs ラムゼーの定理.
- Ramsey's_theorem sameAs 램지의_정리.
- Ramsey's_theorem sameAs Twierdzenie_Ramseya.
- Ramsey's_theorem sameAs Teorema_Finito_de_Ramsey.
- Ramsey's_theorem sameAs m.0197zh.
- Ramsey's_theorem sameAs Q918099.
- Ramsey's_theorem sameAs Q918099.
- Ramsey's_theorem sameAs Ramsey's_theorem.
- Ramsey's_theorem wasDerivedFrom Ramsey's_theorem?oldid=606336229.
- Ramsey's_theorem depiction RamseyTheory_K5_no_mono_K3.svg.
- Ramsey's_theorem isPrimaryTopicOf Ramsey's_theorem.
