Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs
Combinatorics
2018-05-25 v1
Abstract
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.
Cite
@article{arxiv.1805.09394,
title = {Coloring general Kneser graphs and hypergraphs via high-discrepancy hypergraphs},
author = {Jozsef Balogh and Danila Cherkashin and Sergei Kiselev},
journal= {arXiv preprint arXiv:1805.09394},
year = {2018}
}
Comments
9 pages