Proving the Komlós conjecture slowly

The Komlós conjecture was a long-standing open problem in discrepancy theory until it was recently solved in a flurry of AI developments. We give a motivated exposition of an elementary proof of the conjecture due to Karingula and Lovett, as well as a counterexample to the strong Komlós conjecture due to Kintali, aiming to introduce the ideas in a gentle and explained manner in order to ease the understanding of the proofs. We conclude with several problems which remain open.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.03427
Primary Topic
Limits and Structures in Graph Theory
Type
preprint
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preprint

Proving the Komlós conjecture slowly

Lawrence Hollom
arXiv (Cornell University)
Limits and Structures in Graph Theory
preprint

Proving the Komlós conjecture slowly

Lawrence Hollom
preprint en

Abstract

The Komlós conjecture was a long-standing open problem in discrepancy theory until it was recently solved in a flurry of AI developments. We give a motivated exposition of an elementary proof of the conjecture due to Karingula and Lovett, as well as a counterexample to the strong Komlós conjecture due to Kintali, aiming to introduce the ideas in a gentle and explained manner in order to ease the understanding of the proofs. We conclude with several problems which remain open.

arXiv (Cornell University)
Limits and Structures in Graph Theory
DOIOpen Access PDFOpenAlex
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Proving the Komlós conjecture slowly — Lawrence Hollom · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS