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Article

Equitable colorings of hypergraphs with few edges

Discrete Applied Mathematics. 2020. Vol. 276. P. 2-12.
Akhmejanova M., Shabanov D. A.

The paper deals with an extremal problem concerning equitable colorings of uniform hypergraphs. Recall that a vertex coloring of a hypergraph is called proper if there are no monochromatic edges under this coloring. A hypergraph is said to be equitably r-colorable if there is a proper coloring with r colors such that the sizes of any two color classes differ by at most one. In the present paper we prove a new lower for the number of edges for an n-uniform hypergraph taht does not admit an equitable r-coloring.