---
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. Proceedings of the London Mathematical Society. 2025;130(1).
doi:10.1112/plms.70013
apa: Christoph, M., Martinsson, A., Steiner, R., & Wigderson, Y. (2025). Resolution
of the Kohayakawa–Kreuter conjecture. Proceedings of the London Mathematical
Society. Wiley. https://doi.org/10.1112/plms.70013
chicago: Christoph, Micha, Anders Martinsson, Raphael Steiner, and Yuval Wigderson.
“Resolution of the Kohayakawa–Kreuter Conjecture.” Proceedings of the London
Mathematical Society. Wiley, 2025. https://doi.org/10.1112/plms.70013.
ieee: M. Christoph, A. Martinsson, R. Steiner, and Y. Wigderson, “Resolution of
the Kohayakawa–Kreuter conjecture,” Proceedings of the London Mathematical
Society, 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.”
Proceedings of the London Mathematical Society, vol. 130, no. 1, e70013,
Wiley, 2025, doi:10.1112/plms.70013.
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'
fulldoi: https://doi.org/10.1112/plms.70013
intvolume: ' 130'
issue: '1'
language:
- iso: eng
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'
...
---
DOAJ_listed: '1'
OA_place: repository
OA_type: gold
_id: '18951'
abstract:
- lang: eng
text: "We consider local dynamics of the dimer model (perfect matchings) on hypercubic
boxes [n] \r\nd . These consist of successively switching the dimers along alternating
cycles of prescribed (small) lengths. We study the connectivity properties of
the dimer configuration space equipped with these transitions. Answering a question
of Freire, Klivans, Milet, and Saldanha, we show that in three dimensions any
configuration admits an alternating cycle of length at most 6. We further establish
that any configuration on [n] d features order n d−2 alternating cycles of length
at most 4d−2. We also prove that the dynamics of dimer configurations on the unit
hypercube of dimension d is ergodic when switching alternating cycles of length
at most 4d−4. Finally, in the planar but non-bipartite case, we show that parallelogram-shaped
boxes in the triangular lattice are ergodic for switching alternating cycles of
lengths 4 and 6 only, thus improving a result of Kenyon and Rémila, which also
uses 8-cycles. None of our proofs make reference to height functions."
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Ivailo
full_name: Hartarsky, Ivailo
last_name: Hartarsky
- first_name: Lyuben
full_name: Lichev, Lyuben
id: 9aa8388e-d003-11ee-8458-c4c1d7447977
last_name: Lichev
- first_name: Fabio Lucio
full_name: Toninelli, Fabio Lucio
last_name: Toninelli
citation:
ama: Hartarsky I, Lichev L, Toninelli FL. Local dimer dynamics in higher dimensions.
Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions.
2024. doi:10.4171/aihpd/200
apa: Hartarsky, I., Lichev, L., & Toninelli, F. L. (2024). Local dimer dynamics
in higher dimensions. Annales de l’Institut Henri Poincaré D, Combinatorics,
Physics and Their Interactions. EMS Press. https://doi.org/10.4171/aihpd/200
chicago: Hartarsky, Ivailo, Lyuben Lichev, and Fabio Lucio Toninelli. “Local Dimer
Dynamics in Higher Dimensions.” Annales de l’Institut Henri Poincaré D, Combinatorics,
Physics and Their Interactions. EMS Press, 2024. https://doi.org/10.4171/aihpd/200.
ieee: I. Hartarsky, L. Lichev, and F. L. Toninelli, “Local dimer dynamics in higher
dimensions,” Annales de l’Institut Henri Poincaré D, Combinatorics, Physics
and their Interactions. EMS Press, 2024.
ista: Hartarsky I, Lichev L, Toninelli FL. 2024. Local dimer dynamics in higher
dimensions. Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and
their Interactions.
mla: Hartarsky, Ivailo, et al. “Local Dimer Dynamics in Higher Dimensions.” Annales
de l’Institut Henri Poincaré D, Combinatorics, Physics and Their Interactions,
EMS Press, 2024, doi:10.4171/aihpd/200.
short: I. Hartarsky, L. Lichev, F.L. Toninelli, Annales de l’Institut Henri Poincaré
D, Combinatorics, Physics and Their Interactions (2024).
das_tickbox: '1'
date_created: 2025-01-29T10:57:09Z
date_published: 2024-08-26T00:00:00Z
date_updated: 2026-10-16T10:14:21Z
day: '26'
department:
- _id: MaKw
doi: 10.4171/aihpd/200
external_id:
arxiv:
- '2304.10930'
fulldoi: https://doi.org/10.4171/aihpd/200
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2304.10930
mathsc:
- 05B50
- 05C70
- 82C20
month: '08'
oa: 1
oa_version: Preprint
publication: Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their
Interactions
publication_identifier:
eissn:
- 2308-5835
issn:
- 2308-5827
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
researchdata_availability: unclear
scopus_import: '1'
status: public
supplementarymaterial: unclear
title: Local dimer dynamics in higher dimensions
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...