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On the Chromatic Numbers of Random Hypergraphs

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Abstract

The asymptotic behavior of the chromatic number of the binomial random hypergraph \(H(n,k,p)\) is studied in the case when \(k \geqslant 4\) 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.

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Funding

Shabanov acknowledges the support of the Russian Science Foundation, project no. 16-11-10014.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    Yu. A. Demidovich & D. A. Shabanov

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    D. A. Shabanov

  3. Higher School of Economics (National Research University), 101000, Moscow, Russia

    D. A. Shabanov

Authors
  1. Yu. A. Demidovich
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  2. D. A. Shabanov
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Correspondence to Yu. A. Demidovich or D. A. Shabanov.

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Translated by I. Ruzanova

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Demidovich, Y.A., Shabanov, D.A. On the Chromatic Numbers of Random Hypergraphs. Dokl. Math. 102, 380–383 (2020). https://doi.org/10.1134/S1064562420050312

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  • DOI: https://doi.org/10.1134/S1064562420050312

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