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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 502, Pages 37–41
DOI: https://doi.org/10.31857/S268695432201009X (Mi danma235) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On the strong chromatic number of random hypergraphs

T. G. Matveevaa, A. E. Khuzievab, D. A. Shabanovabc

a Lomonosov Moscow State University, Moscow, Russia
b National Research University "Higher School of Economics", Moscow, Russia
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Russia
Citations (1)
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DOI: https://doi.org/10.31857/S268695432201009X
Abstract: The paper deals with the study of the probability threshold for the property of strong colorability with given number of colors of the random $k$-uniform hypergraph in the binomial model $H(n,k,p)$. A vertex coloring of a hypergraph is said to be strong if any edge does not have two vertices of the same color under it. We study the problem of finding the sharp probability threshold of the existence of a strong coloring with $q$ colors for $H(n,k,p)$. By using the second moment method we obtain very tight bounds for this value provided that $q$ is large enough in comparison with $k$.
Keywords: random hypergraph, colorings of hypergraphs, probability thresholds, strong chromatic number, second moment method.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-700-39
Ministry of Science and Higher Education of the Russian Federation МД-1562-2020.1
The second and third authors acknowledge the support of the Russian Foundation for Basic Research, project no. 20-31-70039. The research of the third author was supported by the Russian Federation President Grant, project no. MD-1562.2020.1.
Presented: A. N. Shiryaev
Received: 15.11.2021
Revised: 15.11.2021
Accepted: 20.12.2021
English version:
Doklady Mathematics, 2022, Volume 105, Issue 1, Pages 31–34
DOI: https://doi.org/10.1134/S1064562422010094
Bibliographic databases:
Document Type: Article
UDC: 519.174, 519.179.1, 519.179.4
Language: Russian
Citation: T. G. Matveeva, A. E. Khuzieva, D. A. Shabanov, “On the strong chromatic number of random hypergraphs”, Dokl. RAN. Math. Inf. Proc. Upr., 502 (2022), 37–41; Dokl. Math., 105:1 (2022), 31–34
Citation in format AMSBIB
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\by T.~G.~Matveeva, A.~E.~Khuzieva, D.~A.~Shabanov
\paper On the strong chromatic number of random hypergraphs
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 502
\pages 37--41
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\crossref{https://doi.org/10.31857/S268695432201009X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4448461}
\elib{https://elibrary.ru/item.asp?id=48050924}
\transl
\jour Dokl. Math.
\yr 2022
\vol 105
\issue 1
\pages 31--34
\crossref{https://doi.org/10.1134/S1064562422010094}
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