Geodesic
Equitable colorings of hypergraphs with $r$ colors
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 3-23

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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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     author = {M. Akhmejanova and D. A. Shabanov},
     title = {Equitable colorings of hypergraphs with $r$ colors},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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}
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M. Akhmejanova; D. A. Shabanov. Equitable colorings of hypergraphs with $r$ colors. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 3-23. http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a0/