TY - JOUR
T1 - Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs
AU - Balogh, József
AU - Cherkashin, Danila
AU - Kiselev, Sergei
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2019/6
Y1 - 2019/6
N2 - We suggest a new method for coloring generalized Kneser graphs based on hypergraphs with high discrepancy and a small number of edges. The main result provides 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.
AB - We suggest a new method for coloring generalized Kneser graphs based on hypergraphs with high discrepancy and a small number of edges. The main result provides 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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U2 - 10.1016/j.ejc.2019.03.004
DO - 10.1016/j.ejc.2019.03.004
M3 - Article
AN - SCOPUS:85064090237
SN - 0195-6698
VL - 79
SP - 228
EP - 236
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
ER -