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On the s-Colorful Number of a Random Hypergraph

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Abstract

We study the problem of finding the s-colorful number of a random hypergraph in the binomial model. For different probabilities of the edge appearance, we establish asymptotic bounds for the s-colorful numbers, which hold with probability tending to 1.

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References

  1. N. Alon and J. Spencer, The Probabilistic Method, Wiley, Hoboken (2016).

    MATH  Google Scholar 

  2. M. Dyer, A. Frieze, and C. Greenhill, “On the chromatic number of a random hypergraph,” J. Combin. Theory, Ser. B, 113, 68–122 (2015).

    Article  MathSciNet  Google Scholar 

  3. S. Janson, T. Łuczak, and A. Rucinski, Random Graphs, Wiley, New York (2000).

    Book  Google Scholar 

  4. M. Krivelevich and B. Sudakov, “The chromatic numbers of random hypergraphs,” Random Struct. Algorithms, 12, No. 4, 381–403 (1998).

    Article  MathSciNet  Google Scholar 

  5. A. Kupavskii and D. A. Shabanov, “Colorings of partial Steiners systems and their applications,” J. Math. Sci., 206, No. 5, 511–538 (2015).

    Article  MathSciNet  Google Scholar 

  6. J. P. Schmidt, “Probabilistic analysis of strong hypergraph coloring algorithms and the strong chromatic number,” Discrete Math., 66, 259–277 (1987).

    Article  MathSciNet  Google Scholar 

  7. J. Schmidt-Pruzan, E. Shamir, and E. Upfal, “Random hypergraph coloring algorithms and the weak chromatic number,” J. Graph Theory, 8, 347–362 (1985).

    Article  MathSciNet  Google Scholar 

  8. D. A. Shabanov, “The existence of panchromatic colourings for uniform hypergraphs,” Sb. Math., 201, No. 4, 607–630 (2010).

    Article  MathSciNet  Google Scholar 

  9. D. A. Shabanov, “On the concentration of the chromatic number of a random hypergraph,” Dokl. Math., 96, No. 1, 321–325 (2017).

    Article  MathSciNet  Google Scholar 

  10. E. Shamir, “Chromatic numbers of random hypergraphs and associated graph,” Adv. Comput. Res., 5, 127–142 (1989).

    Google Scholar 

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Moscow, Russia

    D. A. Shabanov

  2. Lomonosov Moscow State University, Moscow, Russia

    D. A. Shabanov

Authors
  1. D. A. Shabanov
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Correspondence to D. A. Shabanov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 3, pp. 191–199, 2018.

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Shabanov, D.A. On the s-Colorful Number of a Random Hypergraph. J Math Sci 254, 582–587 (2021). https://doi.org/10.1007/s10958-021-05327-0

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  • DOI: https://doi.org/10.1007/s10958-021-05327-0

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