A remark on Kashin's discrepancy argument and partial coloring in the Koml\'{o}s conjecture
Combinatorics
2022-08-26 v2 Discrete Mathematics
Data Structures and Algorithms
Metric Geometry
Abstract
In this expository note, we discuss an early partial coloring result of B. Kashin [C. R. Acad. Bulgare Sci., 1985]. Although this result only implies Spencer's six standard deviations [Trans. Amer. Math. Soc., 1985] up to a factor, Kashin's argument gives a simple proof of the existence of a constant discrepancy partial coloring in the setup of Koml\'{o}s conjecture.
Cite
@article{arxiv.2206.08734,
title = {A remark on Kashin's discrepancy argument and partial coloring in the Koml\'{o}s conjecture},
author = {Afonso S. Bandeira and Antoine Maillard and Nikita Zhivotovskiy},
journal= {arXiv preprint arXiv:2206.08734},
year = {2022}
}
Comments
4 pages, an expository note