Ramsey's theorem for pairs

GPTKB entity

Statements (18)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo colorings
infinite sets
graphs
gptkbp:field gptkb:mathematics
combinatorics
gptkbp:generalizes gptkb:Ramsey's_theorem
https://www.w3.org/2000/01/rdf-schema#label Ramsey's theorem for pairs
gptkbp:namedAfter gptkb:Frank_P._Ramsey
gptkbp:publishedIn gptkb:Proceedings_of_the_London_Mathematical_Society
gptkbp:relatedTo gptkb:Ramsey_number
gptkb:Ramsey_theory
gptkb:finite_Ramsey_theorem
gptkb:infinite_Ramsey_theorem
gptkbp:sentence For any coloring of the edges of a complete graph on an infinite set of vertices with two colors, there exists an infinite subset of vertices such that all edges between them have the same color.
gptkbp:yearProved 1930
gptkbp:bfsParent gptkb:Ramsey_theory
gptkbp:bfsLayer 5