The mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. Ramsey theory is named after Frank Plumpton Ramsey, who did seminal work in this area before his untimely death at age 26 in 1930. The theory was subsequently developed extensively by Erdős. The classical problem in Ramsey theory is 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 (i.e., there exists a clique of order m) or at least n will not know each other (i.e., there exists an independent set of order n. Here, R(m, n) is called a Ramsey number.

extremal graph theory | Graham's number | happy end problem | Knuth up-arrow notation | party problem | Ramsey number | structural Ramsey theory