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Random Constructions of Hypergraphs with Large Girth and Without Panchromatic Colorings

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Abstract

We give probabilistic constructions of hypergraphs with large girth that do not admit panchromatic colorings. We prove new upper bounds on the minimal values of the number of edges and the maximum vertex degree in such hypergraphs.

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Authors and Affiliations

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

    A. E. Khuzieva

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  1. A. E. Khuzieva
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Correspondence to A. E. Khuzieva.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 1, pp. 269–283, 2020.

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Khuzieva, A.E. Random Constructions of Hypergraphs with Large Girth and Without Panchromatic Colorings. J Math Sci 262, 581–590 (2022). https://doi.org/10.1007/s10958-022-05838-4

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  • DOI: https://doi.org/10.1007/s10958-022-05838-4

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