Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
Archives

On colorings and isometries

##plugins.themes.bootstrap3.article.main##

Ігор Володимирович Протасов
http://orcid.org/0000-0003-1518-6234

Abstract

In the first section, we prove some isometric versions of the classical Ramsey theorem. In the second section, we discuss open problems on metrically Ramsey ultrafilters. 
Keywords:
Isometric coloring, isometric Ramsey theorem, metrically Ramsey ultrafilters.

##plugins.themes.bootstrap3.article.details##

How to Cite
Протасов, І. (2017). On colorings and isometries. Proceedings of the International Geometry Center, 10(2). https://doi.org/10.15673/tmgc.v10i2.649
Section
Papers
Author Biography

Ігор Володимирович Протасов, Taras Shevchenko National University of Kyiv

Faculty of computer science and cybernetics,

Professor of Operations Research Department

References

1. R. Graham, B. Rotschild, J. Spencer, Ramsey Theory, Willey, New York, 1980.

2. A. Hales, R. Jewett, Regularity and positional games, Trans. Amer. Math. Soc. 106(1963), 222-229.

3. K. Kunen, Combinatories, in: Handbook in Mathematical Logic, Vol.90 (Studies in Logic on Foundations of Mathematics, J. Barwise (editor)), Elsevier, 1982.

4. J. Ne_etril, V. Rdl, Sparse Ramsey Graphs, Combinatorica 4(1984), 71-78.

5. O. Petrenko, I. Protasov, Selective and Ramsey ultra_lters on G- spaces, Notre Dame J. Formal Logic, to appear, preprint (ArXiv: 1310.1827).

6. I.Protasov, Isometric versions of Ramsey theorem, EUREKA, to appear.

7. I.Protasov, K. Protasova Metrically Ramsey ultra_lters, preprint (ArXiv: 1704.07824). 10

8. A. Soifer, ed., Ramsey Theory, Birkhuser, 2011.

9. P. Winkler, Embedding in product of complete graphs, Discrete Appl. Math. 7: 1 (1984) 221-225.