An improvement of the Beck-Fiala theorem
Combinatorics
2015-03-19 v3
Abstract
In 1981 Beck and Fiala proved an upper bound for the discrepancy of a set system of degree d that is independent of the size of the ground set. In the intervening years the bound has been decreased from 2d-2 to 2d-4. We improve the bound to 2d-log* d.
Cite
@article{arxiv.1306.6081,
title = {An improvement of the Beck-Fiala theorem},
author = {Boris Bukh},
journal= {arXiv preprint arXiv:1306.6081},
year = {2015}
}
Comments
18 pages