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)...
62 KB (7,919 words) - 16:19, 31 July 2024
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:...
9 KB (1,139 words) - 20:53, 23 July 2024
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...
38 KB (4,277 words) - 05:12, 12 August 2024
logic, the Paris–Harrington theorem states that a certain claim in Ramsey theory, namely the strengthened finite Ramsey theorem, which is expressible in...
5 KB (648 words) - 20:33, 31 May 2024
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)...
5 KB (622 words) - 13:16, 27 September 2023
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...
10 KB (1,174 words) - 15:57, 18 May 2024
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...
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Frank P. Ramsey, whose theorem, called Ramsey's theorem establishes that ω enjoys a certain property that Ramsey cardinals generalize to the uncountable...
4 KB (550 words) - 10:12, 26 July 2024
Infinitary combinatorics (redirect from Infinite Ramsey theory)
things studied include continuous graphs and trees, extensions of Ramsey's theorem, and Martin's axiom. Recent developments concern combinatorics of the...
10 KB (1,388 words) - 23:25, 6 July 2024
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...
7 KB (1,133 words) - 12:52, 18 August 2023