This post is in response to a comment I got asking about new results in Ramsey theory especially the newer ones.

One thing I would recommend is reading the papers of Ronald Graham on Euclidean Ramsey theory and looking at the bibliographies of these papers and looking at the papers there. His papers are here.

I think there is a preprint on Euclidean Ramsey theory that is submitted. It is a survey on open problems in the field.

Some other recent papers:

“A Note on Euclidean Ramsey Theory”

by James H. Schmerl

Discrete and Computational Geometry

Volume 38, Number 1 / July, 2007

Springer New York

“An Improvement to “A Note on Euclidean Ramsey Theory”

by James H. Schmerl

Discrete and Computational Geometry

Volume 43, Number 2 / March, 2010

“On the chromatic numbers of small-dimensional Euclidean spaces”

by A.B. Kupavskii1, and A.M. Raigorodskii

Electronic Notes

in Discrete Mathematics

Volume 34, 1 August 2009, Pages 435-439

“The chromatic number of the plane: The bounded case”

by Clyde P. Kruskala,

Journal of Computer and System Sciences

Volume 74, Issue 4, June 2008, Pages 598-627

and also one by me:

“All regular polytopes are Ramsey”

by Kristal Cantwell

Journal of Combinatorial Theory, Series A

Volume 114, Issue 3, April 2007, Pages 555-562

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March 27, 2010 at 5:27 pm |

Thank you.

March 31, 2010 at 12:31 pm |

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And want to ask you: is this blog your hobby?

P.S. Sorry for my bad english

April 5, 2010 at 1:37 am |

Thanks!