Euclidean Ramsey Theorems. I
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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
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Journal ArticleDOI
Lines in Euclidean Ramsey Theory
David Conlon,Jacob Fox +1 more
TL;DR: For every natural number n, the existence of a red/blue-coloring of a sequence of m points on a line with consecutive points of distance one is known up to the constant c in the exponent as discussed by the authors.
Journal ArticleDOI
On some problems of Euclidean Ramsey theory
TL;DR: In this paper, it was shown that for any measurable coloring of the euclidean plane with two colours, there is a monochromatic triangle with some restrictions on the sides.
Posted Content
All finite sets are Ramsey in the maximum norm.
Andrey Kupavskii,A. A. Sagdeev +1 more
TL;DR: In this paper, it was shown that the chromatic number of the points of a metric space with no monochromatic copy of the corresponding points of another metric space grows exponentially with the number of points.
Book ChapterDOI
Open Problems in Euclidean Ramsey Theory
Ron Graham,Eric Tressler +1 more
TL;DR: Ramsey theory is the study of structure that must exist in a system, most typically after it has been partitioned as discussed by the authors, and it is the most commonly used theory in computer science.
References
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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.