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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 254–272 (Mi mz4304)  

On a Series of Problems Related to the Borsuk and Nelson–Erdős–Hadwiger Problems

A. M. Raigorodskii, M. M. Kityaev

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

Abstract: In the present paper, a series of problems connecting the Borsuk and Nelson–Erdős–Hadwiger classical problems in combinatorial geometry is considered. The problem has to do with finding the number $\chi(n,a,d)$ equal to the minimal number of colors needed to color an arbitrary set of diameter $d$ in $n$-dimensional Euclidean space in such a way that the distance between points of the same color cannot be equal to $a$. Some new lower bounds for the quantity $\chi(n,a,d)$ are obtained.

Keywords: Borsuk problem, Nelson–Erdős–Hadwiger problem, chromatic number, Stirling formula, infinite graph, Euclidean space, distribution of primes

DOI: https://doi.org/10.4213/mzm4304

Full text: PDF file (615 kB)
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English version:
Mathematical Notes, 2008, 84:2, 239–255

Bibliographic databases:

UDC: 514
Received: 10.04.2007

Citation: A. M. Raigorodskii, M. M. Kityaev, “On a Series of Problems Related to the Borsuk and Nelson–Erdős–Hadwiger Problems”, Mat. Zametki, 84:2 (2008), 254–272; Math. Notes, 84:2 (2008), 239–255

Citation in format AMSBIB
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