Geodesic
On balanced colorings of hypergraphs
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 141-163.

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The paper deals with an extremal problem concerning hypergraph colorings. Let $k$ be an integer. The problem is to find the value $m_k(n)$ equal to the minimum number of edges in an $n$-uniform hypergraph not admitting two-colorings of the vertex set such that every edge of the hypergraph contains $k$ vertices of each color. In this paper, we obtain the exact values of $m_2(5)$ and $m_2(4)$, and the upper bounds for $m_3(7)$ and $m_4(9)$. 
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A. P. Rozovskaya; M. V. Titova; D. A. Shabanov. On balanced colorings of hypergraphs. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 7, pp. 141-163. http://geodesic.mathdoc.fr/item/FPM_2009_15_7_a6/

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