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Mat. Zametki, 2018, Volume 103, Issue 2, Pages 248–257 (Mi mz11397)  

This article is cited in 5 scientific papers (total in 5 papers)

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.

DOI: https://doi.org/10.4213/mzm11397

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

Bibliographic databases:

UDC: 514.17
Received: 01.10.2016
Revised: 07.02.2017

Citation: R. I. Prosanov, “Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets”, Mat. Zametki, 103:2 (2018), 248–257; Math. Notes, 103:2 (2018), 243–250

Citation in format AMSBIB
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\pages 248--257
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Sagdeev, “Improved Frankl–Rödl theorem and some of its geometric consequences”, Problems Inform. Transmission, 54:2 (2018), 139–164  mathnet  crossref  isi  elib
    2. A. Sagdeev, “On the Frankl–Rödl theorem”, Izv. Math., 82:6 (2018), 1196–1224  mathnet  crossref  crossref  adsnasa  isi  elib
    3. A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396  mathnet  crossref  isi
    4. A. A. Sagdeev, “O khromaticheskikh chislakh, sootvetstvuyuschikh eksponentsialno ramseevskim mnozhestvam”, Kombinatorika i teoriya grafov. X, Zap. nauchn. sem. POMI, 475, POMI, SPb., 2018, 174–189  mathnet
    5. L. I. Bogolubsky, A. M. Raigorodskii, “A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics $\ell_1$ and $\ell_2$”, Math. Notes, 105:2 (2019), 180–203  mathnet  crossref  crossref  isi  elib
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