In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)...

red triangle? It turns out that the answer is 6. See the article on Ramsey's theorem for a rigorous proof. Another way to express this result is as follows:...

theorem appealing. In 1930, in a paper entitled 'On a Problem of Formal Logic,' Frank P. Ramsey proved a very general theorem (now known as Ramsey's theorem)...

logic, the Paris–Harrington theorem states that a certain claim in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in...

area of mathematics known as Ramsey theory, a Ramsey class is one which satisfies a generalization of Ramsey's theorem. Suppose A {\displaystyle A} ...

Ramsey-Turán theory is a subfield of extremal graph theory. It studies common generalizations of Ramsey's theorem and Turán's theorem. In brief, Ramsey-Turán...

finitary result that makes precise one of the corollaries of Ramsey's theorem. While Ramsey's theorem makes it easy to prove that every infinite sequence of...

a Problem of Formal Logic now bears his name (Ramsey's theorem). While this theorem is the work Ramsey is probably best remembered for, he proved it only...

a second color for E2 to obtain a triangle-free edge coloring. By Ramsey's theorem, for any finite number k of colors, there exists a number n such that...

In mathematics, the Graham–Rothschild theorem is a theorem that applies Ramsey theory to combinatorics on words and combinatorial cubes. It is named after...

things studied include continuous graphs and trees, extensions of Ramsey's theorem, and Martin's axiom. Recent developments concern combinatorics of the...

Frank P. Ramsey, whose theorem, called Ramsey's theorem establishes that ω enjoys a certain property that Ramsey cardinals generalize to the uncountable...

In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in...

graph theorem (graph theory) Perlis theorem (graph theory) Planar separator theorem (graph theory) Pólya enumeration theorem (combinatorics) Ramsey's theorem...

Rado's theorem is a theorem from the branch of mathematics known as Ramsey theory. It is named for the German mathematician Richard Rado. It was proved...

theory, a branch of mathematics, the Erdős–Rado theorem is a basic result extending Ramsey's theorem to uncountable sets. It is named after Paul Erdős...

mathematics, the Milliken–Taylor theorem in combinatorics is a generalization of both Ramsey's theorem and Hindman's theorem. It is named after Keith Milliken...

Milliken–Taylor theorem is a common generalisation of Hindman's theorem and Ramsey's theorem. The definition of being IP has been extended from subsets of the special...

) {\displaystyle dis(X)\geq \Delta (X)} . There is an analogue of Ramsey's theorem from combinatorics for polyadic spaces. For this, we describe the relationship...

to Simmons. They called it the Ramsey game, since it is closely related to Ramsey's theorem (see below). Ramsey's theorem implies that, whenever we color...

extended to a total function. Various theorems in combinatorics, such as certain forms of Ramsey's theorem.Theorem III.7.2 The system ATR0 adds to ACA0...

value theorem Multivariate normal distribution (to do) Holomorphic functions are analytic Pythagorean theorem Quadratic equation Quotient rule Ramsey's theorem...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

of Man Ramsey High School, New Jersey, U.S. The Ramsey Academy, Halstead, Essex, England Ramsey theory, a branch mathematics Ramsey's theorem, in combinatorics...

{\displaystyle r} pieces. Here are some of the classic results of Ramsey theory: (Finite) Ramsey's theorem: for every k ≤ m , r ∈ N {\displaystyle k\leq m,r\in \mathbb...

Incidence coloring List coloring List edge-coloring Perfect graph Ramsey's theorem Sperner's lemma Strong coloring Subcoloring Tait's conjecture Total...

also χ {\displaystyle \chi } -bounded, as Ramsey's theorem implies that they have large cliques. Vizing's theorem can be interpreted as stating that the...

In mathematics, Milliken's tree theorem in combinatorics is a partition theorem generalizing Ramsey's theorem to infinite trees, objects with more structure...

cardinal arithmetic and the study of extensions of Ramsey's theorem such as the Erdős–Rado theorem. Descriptive set theory is the study of subsets of...

ISBN 978-0-393-02023-6. Graham, R. L.; Rothschild, B. L. (1971). "Ramsey's Theorem for n-Parameter Sets" (PDF). Transactions of the American Mathematical...