Ramsey's theorem
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English
[edit]Etymology
[edit]Named after British mathematician and philosopher Frank P. Ramsey.
Noun
[edit]Ramsey's theorem (countable and uncountable, plural Ramsey's theorems)
- (mathematics) A (version of a) theorem concerning the existence of cliques in a labelled complete graph.
- The theorem that any graph labelling (with colours) of a sufficiently large complete graph contains monochromatic cliques.
- The theorem that any graph labelling (with colours) of an infinite complete graph contains at least one infinite monochromatic clique.
Usage notes
[edit]Equivalent statements exist for other mathematical contexts. For instance, for a combinatoric statement of the infinitary version: If is a partition of , then there exists an infinite subset that is homogeneous for the partition (i.e., for some ).
Synonyms
[edit]- (finite version of theorem): finite Ramsey's theorem
- (infinite version of theorem): infinite Ramsey's theorem
Further reading
[edit]- Infinitary combinatorics on Wikipedia.Wikipedia
- Ramsey theory on Wikipedia.Wikipedia
- Van der Waerden number on Wikipedia.Wikipedia