This article is cited in 19 papers

On the Ramsey numbers for complete distance graphs with vertices in $\{0,1\}^n$

K. A. Mikhailov, A. M. Raigorodskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A new problem of Ramsey type is posed for complete distance graphs in $\mathbb R^n$ with vertices in the Boolean cube. This problem is closely related to the classical Nelson-Erdős-Hadwiger problem on the chromatic number of a space. Several quite sharp estimates are obtained for certain numerical characteristics that appear in the framework of the problem.
Bibliography: 15 titles.

Keywords: Ramsey numbers, distance graphs, chromatic number.

UDC: 519.112.4+519.174

MSC: Primary 05C55; Secondary 05C15, 05C80

Received: 04.06.2008

DOI: 10.4213/sm6373

 English version: Sbornik: Mathematics, 2009, 200:12, 1789–1806

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