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Teoriya Veroyatnostei i ee Primeneniya, 2022, Volume 67, Issue 2, Pages 223–246
DOI: https://doi.org/10.4213/tvp5458
(Mi tvp5458)
 

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

On two limit values of the chromatic number of a random hypergraph

Yu. A. Demidovicha, D. A. Shabanovbc

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
c Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (476 kB) Citations (1)
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Abstract: The limit concentration of the values of the chromatic number of the random hypergraph $H(n,k,p)$ in the binomial model is studied. It is proved that, for a fixed $k\ge 3$ and with not too rapidly increasing $n^{k-1}p$, the chromatic number of the hypergraph $H(n,k,p)$ lies, with probability tending to $1$, in the set of two consecutive values. Moreover, it is shown that, under slightly stronger constraints on the growth of $n^{k-1}p$, these values can be explicitly evaluated as functions of $n$ and $p$.
Keywords: random hypergraph, chromatic number, second moment method.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-70039
Ministry of Science and Higher Education of the Russian Federation МД-1562.2020.1
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant 20-31-70039). The second author was supported by the grant of the President of Russian Federation MD-1562.2020.1.
Received: 18.11.2020
Revised: 22.10.2021
Accepted: 24.10.2021
English version:
Theory of Probability and its Applications, 2022, Volume 67, Issue 2, Pages 175–193
DOI: https://doi.org/10.1137/S0040585X97T990861
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. A. Demidovich, D. A. Shabanov, “On two limit values of the chromatic number of a random hypergraph”, Teor. Veroyatnost. i Primenen., 67:2 (2022), 223–246; Theory Probab. Appl., 67:2 (2022), 175–193
Citation in format AMSBIB
\Bibitem{DemSha22}
\by Yu.~A.~Demidovich, D.~A.~Shabanov
\paper On two limit values of the chromatic number of a~random hypergraph
\jour Teor. Veroyatnost. i Primenen.
\yr 2022
\vol 67
\issue 2
\pages 223--246
\mathnet{http://mi.mathnet.ru/tvp5458}
\crossref{https://doi.org/10.4213/tvp5458}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4466428}
\zmath{https://zbmath.org/?q=an:7573879}
\transl
\jour Theory Probab. Appl.
\yr 2022
\vol 67
\issue 2
\pages 175--193
\crossref{https://doi.org/10.1137/S0040585X97T990861}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85161851600}
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  • https://www.mathnet.ru/eng/tvp5458
  • https://doi.org/10.4213/tvp5458
  • https://www.mathnet.ru/eng/tvp/v67/i2/p223
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
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