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)...

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...

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...

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...

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

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 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...

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

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...

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

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

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...

) {\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...

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

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...

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...

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...

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

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

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

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

1007/BF01113568. S2CID 120230682. Chvatal, V.; Erdös, P.; Hedrlín, Z. (1972). "Ramsey's theorem and self-complementary graphs". Discrete Mathematics. 3 (4): 301–304...

linearly ordered set X as a set of indiscernibles. The proof uses Ramsey's theorem. The Ehrenfeucht–Mostowski is used to construct models with many automorphisms...

different colors, there is bound to be a monochromatic triangle; see Ramsey's theorem. Either 16 or 18 unit squares can be formed into rectangles with perimeter...

principles that do not fit neatly into this framework, like RT2 2 (Ramsey's theorem for pairs). Research in reverse mathematics often incorporates methods...

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

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...

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