Ramsey's theorem

English Etymology Named after British mathematician and philosopher Frank P. Ramsey. Noun ~ en 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 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 finite version of theorem finite Ramsey's theorem infinite version of theorem infinite Ramsey's theorem Further reading Infinitary combinatorics Ramsey theory Van der Waerden number en eponyms