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Colorings of Partial Steiner Systems and Their Applications

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Abstract

This paper deals with extremal problems concerning colorings of partial Steiner systems. We establish a new sufficient condition for r-colorability of a hypergraph from some class of such systems in terms of maximum vertex degree. Moreover, as a corollary we obtain a new lower bound for the threshold probability for r-colorability of a random hypergraph in a binomial model.

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Correspondence to A. Kupavskii.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 3, pp. 77–115, 2013.

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Kupavskii, A., Shabanov, D.A. Colorings of Partial Steiner Systems and Their Applications. J Math Sci 206, 511–538 (2015). https://doi.org/10.1007/s10958-015-2330-8

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Keywords

  • Random Graph
  • Chromatic Number
  • Threshold Probability
  • Random Subset
  • Steiner System