The Ramsey number R(m, n), sometimes also denoted r(s, t) (e.g., Mattheus and Verstraete 2023), 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 (i.e., have clique number m or independence number 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).
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