---
OA_place: repository
OA_type: green
_id: '22157'
abstract:
- lang: eng
  text: "A graph \U0001D43A is said to be Ramsey for a tuple of graphs(\U0001D43B
    1 , … , \U0001D43B\U0001D45F ) if every \U0001D45F-coloring of the edges of \U0001D43A
    con-tains a monochromatic copy of \U0001D43B\U0001D456 in color \U0001D456, for
    some \U0001D456.A fundamental question at the intersection of Ramseytheory and
    the theory of random graphs is to deter-mine the threshold at which the binomial
    randomgraph \U0001D43A\U0001D45B,\U0001D45D becomes asymptotically almost surely
    Ram-sey for a fixed tuple (\U0001D43B 1 , … , \U0001D43B\U0001D45F ), and a famous
    conjectureof Kohayakawa and Kreuter predicts this threshold.Earlier work of Mousset–Nenadov–Samotij,
    Bowtell–Hancock–Hyde, and Kuperwasser–Samotij–Wigdersonhas reduced this probabilistic
    problem to a determinis-tic graph decomposition conjecture. In this paper, weresolve
    this deterministic problem, thus proving theKohayakawa–Kreuter conjecture. Along
    the way, weprove a number of novel graph decomposition resultsthat may be of independent
    interest."
article_number: e70013
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Micha
  full_name: Christoph, Micha
  last_name: Christoph
- first_name: Anders
  full_name: Martinsson, Anders
  last_name: Martinsson
- first_name: Raphael
  full_name: Steiner, Raphael
  last_name: Steiner
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
citation:
  ama: Christoph M, Martinsson A, Steiner R, Wigderson Y. Resolution of the Kohayakawa–Kreuter
    conjecture. <i>Proceedings of the London Mathematical Society</i>. 2025;130(1).
    doi:<a href="https://doi.org/10.1112/plms.70013">10.1112/plms.70013</a>
  apa: Christoph, M., Martinsson, A., Steiner, R., &#38; Wigderson, Y. (2025). Resolution
    of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical
    Society</i>. Wiley. <a href="https://doi.org/10.1112/plms.70013">https://doi.org/10.1112/plms.70013</a>
  chicago: Christoph, Micha, Anders Martinsson, Raphael Steiner, and Yuval Wigderson.
    “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London
    Mathematical Society</i>. Wiley, 2025. <a href="https://doi.org/10.1112/plms.70013">https://doi.org/10.1112/plms.70013</a>.
  ieee: M. Christoph, A. Martinsson, R. Steiner, and Y. Wigderson, “Resolution of
    the Kohayakawa–Kreuter conjecture,” <i>Proceedings of the London Mathematical
    Society</i>, vol. 130, no. 1. Wiley, 2025.
  ista: Christoph M, Martinsson A, Steiner R, Wigderson Y. 2025. Resolution of the
    Kohayakawa–Kreuter conjecture. Proceedings of the London Mathematical Society.
    130(1), e70013.
  mla: Christoph, Micha, et al. “Resolution of the Kohayakawa–Kreuter Conjecture.”
    <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1, e70013,
    Wiley, 2025, doi:<a href="https://doi.org/10.1112/plms.70013">10.1112/plms.70013</a>.
  short: M. Christoph, A. Martinsson, R. Steiner, Y. Wigderson, Proceedings of the
    London Mathematical Society 130 (2025).
date_created: 2026-06-29T10:50:35Z
date_published: 2025-01-01T00:00:00Z
date_updated: 2026-07-08T10:24:21Z
day: '01'
ddc:
- '500'
doi: 10.1112/plms.70013
extern: '1'
external_id:
  arxiv:
  - '2402.03045'
intvolume: '       130'
issue: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2402.03045
mathsc:
- 05C70
- 05D10
- 05C80
month: '01'
oa: 1
oa_version: Preprint
publication: Proceedings of the London Mathematical Society
publication_identifier:
  eissn:
  - 1460-244X
  issn:
  - 0024-6115
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Resolution of the Kohayakawa–Kreuter conjecture
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 130
year: '2025'
...