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

This article is cited in 1 scientific paper (total in 1 paper)

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_а
Ministry of Education and Science of the Russian Federation НШ-6760.2018.1


Full text: PDF file (237 kB)
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UDC: 517
Received: 12.11.2018

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  mathnet  crossref  crossref  isi  elib
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