The Ramsey number R(m, n) gives the solution to the party problem, which asks the minimum number of guests R(m, n) that must be invited so that at least m will know each other or at least n will not know each other. In the language of graph theory, the Ramsey number is the minimum number of vertices v = R(m, n) such that all undirected simple graphs of order v contain a clique of order m or an independent set of order n. Ramsey's theorem states that such a number exists for all m and n. By symmetry, it is true that R(m, n) = R(n, m).

clique | clique number | complete graph | extremal graph | independence number | independent set | irredundant Ramsey number | Ramsey's theorem | Ramsey theory | Schur number