Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs

@article{Balogh2019ColoringGK,
  title={Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs},
  author={Jozsef Balogh and Danila D. Cherkashin and Sergei Kiselev},
  journal={Eur. J. Comb.},
  year={2019},
  volume={79},
  pages={228-236}
}
  • Jozsef Balogh, Danila D. Cherkashin, Sergei Kiselev
  • Published 2019
  • Mathematics, Computer Science
  • Eur. J. Comb.
  • We suggest a new method on coloring generalized Kneser graphs based on hypergraphs with high discrepancy and small number of edges. The main result is providing a proper coloring of K(n, n/2-t, s) in (4 + o(1))(s + t)^2 colors, which is produced by Hadamard matrices. Also, we show that for colorings by independent set of a natural type, this result is the best possible up to a multiplicative constant. Our method extends to Kneser hypergraphs as well. 

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