The theorem that any graph labelling (with colours) of a sufficiently large complete graph contains monochromatic cliques.

plural of Ramsey's theorem

(graph theory) A characterization of the connectivity in finite undirected graphs in terms of the minimum number of disjoint paths that can be found between any pair of vertices.

(mathematics) A basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism.

(number theory) A theorem stating that the sum of the reciprocals of the twin primes converges to a finite value (Brun's constant).

(number theory) A theorem that gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for a given degree of smoothness, and provides a method for finding all such pairs using Pell equations.

An important limitative theorem in quantum computing that establishes an upper bound (Holevo's bound) for the amount of information that can be known about a quantum state.

(mathematics) A result concerning certain infinite-dimensional vector spaces, stating that any orthomodular form that has an infinite orthonormal sequence is a Hilbert space over the real numbers, complex numbers or quaternions.

(computing theory) A theorem giving a relationship between deterministic and non-deterministic space complexity.

(mathematics) A theorem used in complex analysis to establish a bound on the growth rates for an analytic function.