scholarly journals A Euclidean Ramsey Result in the Plane

10.37236/7148 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Sergei Tsaturian
Keyword(s):  
Elementary Proof ◽  
Ramsey Theory ◽  
Unit Distance ◽  
Euclidean Ramsey Theory

An old question in Euclidean Ramsey theory asks, if the points in the plane are red-blue coloured, does there always exist a red pair of points at unit distance or five blue points in line separated by unit distances? An elementary proof answers this question in the affirmative.

Open Problems in Euclidean Ramsey Theory

Ramsey Theory ◽  
2011 ◽  
pp. 115-120
Author(s):  
Ron Graham ◽  
Eric Tressler
Keyword(s):  
Ramsey Theory ◽  
Open Problems ◽  
Euclidean Ramsey Theory

scholarly journals A Note on Euclidean Ramsey Theory

2007 ◽  
Vol 38 (1) ◽  
pp. 155-167 ◽  
Author(s):  
James H. Schmerl
Keyword(s):  
Ramsey Theory ◽  
Euclidean Ramsey Theory

scholarly journals Hypergraph list coloring and Euclidean Ramsey theory

2011 ◽  
Vol 39 (3) ◽  
pp. 377-390 ◽  
Author(s):  
Noga Alon ◽  
Alexandr Kostochka
Keyword(s):  
Ramsey Theory ◽  
List Coloring ◽  
Euclidean Ramsey Theory

Open Problems Column Edited by William Gasarch This Issue's Column!

2021 ◽  
Vol 51 (4) ◽  
pp. 30-46
Author(s):  
William Gasarch
Keyword(s):  
Elementary Proof ◽  
Ramsey Theory ◽  
Open Problems ◽  
General Theme ◽  
Open Questions ◽  
Ramsey Type

In this column we state a class of open problems in Ramsey Theory. The general theme is to take Ramsey-type statements that are false and weaken them by allowing the homogenous set to use more than one color. This concept is not new, and the theorems we state and/or prove are not new; however, the open questions that request easier proofs of the known theorems (or weaker versions) may be new. We use the phrase an elementary proof. This is not meant to be a technical or rigorous term. What we really mean is a proof that can be taught in an undergraduate combinatorics course. A good example of what we mean is the proof of Theorem 9.3.

Sign in / Sign up

Export Citation Format

Share Document