Euclidean Ramsey Theorems. I
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TLDR
Questions of whether or not certain R are r -Ramsey where B is a Euclidean space and R is defined geometrically are investigated.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1973-05-01 and is currently open access. It has received 115 citations till now. The article focuses on the topics: Euclidean space.read more
Citations
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Book ChapterDOI
Euclidean Distance Graphs on the Rational Points
TL;DR: In this article, the usual rings of integers, rational numbers, and real numbers, respectively, are represented as follows: if X is a set and n is a positive integer, X n denotes, as usual, the set of n-tuples with entries from X.
Euclidean Gallai-Ramsey Theory
Yaping Mao,Kenta Oeki,Zhao Wang +2 more
TL;DR: In this article , Euclidean Gallai-Ramsey theory was introduced by combining the EGM theory and the Grams theory on graphs, and a bound on n 0 was given for some configurations K and K ⊆ , such as triangles and rectangles, where the purpose is to find a monochromatic con�guration.
Proceedings Article
Almost-Monochromatic Sets and the Chromatic Number of the Plane.
TL;DR: In this article, the authors consider the problem of finding almost monochromatic similar copies of pairs of pairs in colourings of the same colouring of a pair of colours in the same set of colours.
Proceedings Article
Approximate euclidean ramsey theorems.
TL;DR: In this paper, the authors generalize the results of Szemeredi and Katznelson for separated point sets on the line and respectively in the Euclidean space, and show that every sufficiently large separated set of points in such a space contains an arbitrary large subset of almost collinear points.
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Journal ArticleDOI
On a Problem of Formal Logic
TL;DR: This paper is primarily concerned with a special case of one of the leading problems of mathematical logic, the problem of finding a regular procedure to determine the truth or falsity of any given logical formula.
Journal ArticleDOI
Regularity and Positional Games
A. W. Hales,R. I. Jewett +1 more
TL;DR: In this paper, it was shown that a set is n-regular in X if, for any partition of X into N parts, some part has as a subset a member of the set.