PreprintCC BY 4.0arXiv
An elementary proof of the Komlós conjecture
Abstract
We give an elementary proof of the Komlós conjecture by simplifying the recent proof of Guo, Fang, and Lu. We show that any vectors v1,…,vn∈ℝd with |vi|2≤1 admit signs εi∈{−1,1} such that |∑i=1nεi vi|∞≤36. The proof uses only elementary combinatorial and probabilistic arguments and basic calculus.
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BibTeX
@misc{karingula2026elementary,
title = {{An elementary proof of the Komlós conjecture}},
author = {Sankeerth Rao Karingula and Shachar Lovett},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20979},
eprint = {2609.20979},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20979},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An elementary proof of the Komlós conjecture
AU - Sankeerth Rao Karingula
AU - Shachar Lovett
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.20979
UR - https://arxiv.org/abs/2609.20979
AB - We give an elementary proof of the Komlós conjecture by simplifying the recent proof of Guo, Fang, and Lu. We show that any vectors v_1,…,v_n∈ℝ^d with |v_i|_2≤1 admit signs ε_i∈{−1,1} such that |∑_i=1^nε_i v_i|_∞≤36. The proof uses only elementary combinatorial and probabilistic arguments and basic calculus.
ER -