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Equitable Colorings of Hypergraphs with r Colors

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Abstract

The paper deals with a problem concerning equitable vertex colorings of uniform hypergraphs, i.e., colorings under which there are no monochromatic edges and simultaneously all the color classes have almost the same cardinalities. We obtain a new bound on the edge number of an n-uniform hypergraph that guarantees the existence of an equitable vertex coloring with r colors for this hypergraph.

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Authors and Affiliations

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

    M. Akhmejanova & D. A. Shabanov

  2. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

    D. A. Shabanov

Authors
  1. M. Akhmejanova
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  2. D. A. Shabanov
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Corresponding author

Correspondence to M. Akhmejanova.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 23, No. 1, pp. 3–23, 2020.

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Akhmejanova, M., Shabanov, D.A. Equitable Colorings of Hypergraphs with r Colors. J Math Sci 262, 391–405 (2022). https://doi.org/10.1007/s10958-022-05823-x

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  • DOI: https://doi.org/10.1007/s10958-022-05823-x

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