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This article is cited in 10 scientific papers (total in 10 papers)
On the Frankl–Rödl theorem
A. Sagdeev
Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
Abstract:
In this paper we considerably strengthen the currently known explicit
exponential lower bound for the chromatic number of a Euclidean space with
a forbidden regular simplex. We also strengthen the exponential lower bound
for the chromatic numbers of distance graphs with large girth.
Keywords:
Frankl–Rödl theorem, Euclidean Ramsey theory, distance graph, chromatic number, girth.
DOI:
https://doi.org/10.4213/im8630
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English version:
Izvestiya: Mathematics, 2018, 82:6, 1196–1224
Bibliographic databases:
   
UDC:
517
MSC: 05C15, 05C12, 05D10
Received: 18.11.2016
Revised: 09.04.2018
Citation:
A. Sagdeev, “On the Frankl–Rödl theorem”, Izv. RAN. Ser. Mat., 82:6 (2018), 128–157; Izv. Math., 82:6 (2018), 1196–1224
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/izv8630https://doi.org/10.4213/im8630 http://mi.mathnet.ru/eng/izv/v82/i6/p128
Citing articles on Google Scholar:
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Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396
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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
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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
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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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R. I. Prosanov, “Counterexamples to Borsuk's Conjecture with Large Girth”, Math. Notes, 105:6 (2019), 874–880
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A. A. Sagdeev, “On the Partition of an Odd Number into Three Primes in a Prescribed Proportion”, Math. Notes, 106:1 (2019), 98–107
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A. A. Sagdeev, “On a Frankl–Wilson Theorem”, Problems Inform. Transmission, 55:4 (2019), 376–395
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A. A. Sagdeev, A. M. Raigorodskii, “On a Frankl-Wilson theorem and its geometric corollaries”, Acta Math. Univ. Comenian. (N.S.), 88:3 (2019), 1029–1033
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Ph. A. Pushnyakov, A. M. Raigorodskii, “Estimate of the Number of Edges in Special Subgraphs of a Distance Graph”, Math. Notes, 107:2 (2020), 322–332
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Prosanov R., “a New Proof of the Larman-Rogers Upper Bound For the Chromatic Number of the Euclidean Space”, Discret Appl. Math., 276:SI (2020), 115–120
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