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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 494, Pages 30–34
DOI: https://doi.org/10.31857/S2686954320050331 (Mi danma112) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On the chromatic numbers of random hypergraphs

Yu. A. Demidovicha, D. A. Shabanovabc

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow oblast, Russian Federation
b Lomonosov Moscow State University, Moscow, Russian Federation
c National Research University "Higher School of Economics", Moscow, Russian Federation
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DOI: https://doi.org/10.31857/S2686954320050331
Abstract: The asymptotic behavior of the chromatic number of the binomial random hypergraph $H(n,k,p)$ is studied in the case when $k\ge4$ is fixed, $n$ tends to infinity, and $p=p(n)$ is a function. If $p=p(n)$ does not decrease too slowly, we prove that the chromatic number of $H(n,k,p)$ is concentrated in two or three consecutive values, which can be found explicitly as functions of $n$, $p$ and $k$.
Keywords: random hypergraph, chromatic number, second moment method.
Funding agency Grant number
Russian Science Foundation 16–11–10014
Shabanov acknowledges the support of the Russian Science Foundation, project no. 16-11-10014.
Presented: A. N. Shiryaev
Received: 26.11.2019
Revised: 26.11.2019
Accepted: 23.06.2020
English version:
Doklady Mathematics, 2020, Volume 102, Issue 2, Pages 380–383
DOI: https://doi.org/10.1134/S1064562420050312
Bibliographic databases:
Document Type: Article
UDC: 519.174, 519.179.1, 519.179.4
Language: Russian
Citation: Yu. A. Demidovich, D. A. Shabanov, “On the chromatic numbers of random hypergraphs”, Dokl. RAN. Math. Inf. Proc. Upr., 494 (2020), 30–34; Dokl. Math., 102:2 (2020), 380–383
Citation in format AMSBIB
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\by Yu.~A.~Demidovich, D.~A.~Shabanov
\paper On the chromatic numbers of random hypergraphs
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\pages 30--34
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\crossref{https://doi.org/10.31857/S2686954320050331}
\zmath{https://zbmath.org/?q=an:1478.05134}
\elib{https://elibrary.ru/item.asp?id=44344643}
\transl
\jour Dokl. Math.
\yr 2020
\vol 102
\issue 2
\pages 380--383
\crossref{https://doi.org/10.1134/S1064562420050312}
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