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On balanced colorings of hypergraphs

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Abstract

This 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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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. P. Rozovskaya, M. V. Titova & D. A. Shabanov

Authors
  1. A. P. Rozovskaya
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  2. M. V. Titova
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  3. D. A. Shabanov
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Corresponding author

Correspondence to A. P. Rozovskaya.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 7, pp. 141–163, 2009.

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Rozovskaya, A.P., Titova, M.V. & Shabanov, D.A. On balanced colorings of hypergraphs. J Math Sci 169, 654–670 (2010). https://doi.org/10.1007/s10958-010-0067-y

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  • DOI: https://doi.org/10.1007/s10958-010-0067-y

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