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On Equitable Colorings of Hypergraphs

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Abstract

A two-coloring is said to be equitable if, on the one hand, there are no monochromatic edges (the coloring is regular) and, on the other hand, the cardinalities of color classes differ from one another by at most 1. It is proved that, for the existence of an equitable two-coloring, it suffices that the number of edges satisfy an estimate of the same order as that for a regular coloring. This result strengthens the previously known Radhakrishnan-Srinivasan theorem.

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Authors and Affiliations

  1. Advanced Combinatorics and Network Applications Laboratory, Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Oblast, 141701, Russia

    M. Akhmejanova

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  1. M. Akhmejanova
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Correspondence to M. Akhmejanova.

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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 3, pp. 323–332.

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Akhmejanova, M. On Equitable Colorings of Hypergraphs. Math Notes 106, 319–326 (2019). https://doi.org/10.1134/S0001434619090013

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  • DOI: https://doi.org/10.1134/S0001434619090013

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