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Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets

R. I. Prosanov

Lomonosov Moscow State University

Abstract: The chromatic number of a Euclidean space $\mathbb R^n$ with a forbidden finite set $C$ of points is the least number of colors required to color the points of this space so that no monochromatic set is congruent to $C$. New upper bounds for this quantity are found.

Keywords: Euclidean Ramsey theory, chromatic number of space.

UDC: 514.17

Received: 01.10.2016
Revised: 07.02.2017

DOI: 10.4213/mzm11397

 English version: Mathematical Notes, 2018, 103:2, 243–250

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