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 Zap. Nauchn. Sem. POMI, 2018, Volume 475, Pages 174–189 (Mi znsl6690)

On the chromatic numbers corresponding to exponentially Ramsey sets

A. A. Sagdeev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, Russia

Abstract: In this paper, nontrivial upper bounds on the chromatic numbers of the spaces $\mathbb{R}^n_p=(\mathbb{R}^n, l_p)$ with forbidden monochromatic sets are proved. In the case of forbidden rectangular parallelepiped or a regular simplex, explicit exponential lower bounds on the chromatic numbers are obtained. Exact values of the chromatic numbers of the spaces $\mathbb{R}^n_p$ with forbidden regular simplex in case $p = \infty$ are found.

Key words and phrases: chromatic number, Euclidean Ramsey theory, exponentially Ramsey set, regular simplex.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00355_à Ministry of Education and Science of the Russian Federation ÍØ-6760.2018.1

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Citation: A. A. Sagdeev, “On the chromatic numbers corresponding to exponentially Ramsey sets”, Combinatorics and graph theory. Part X, Zap. Nauchn. Sem. POMI, 475, POMI, St. Petersburg, 2018, 174–189

Citation in format AMSBIB
\Bibitem{Sag18} \by A.~A.~Sagdeev \paper On the chromatic numbers corresponding to exponentially Ramsey sets \inbook Combinatorics and graph theory. Part~X \serial Zap. Nauchn. Sem. POMI \yr 2018 \vol 475 \pages 174--189 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6690} 

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This publication is cited in the following articles:
1. Ph. A. Pushnyakov, “The Number of Edges in Induced Subgraphs of Some Distance Graphs”, Math. Notes, 105:4 (2019), 582–591
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