---
OA_place: publisher
OA_type: hybrid
_id: '22152'
abstract:
- lang: eng
  text: "We study off-diagonal Ramsey numbers \U0001D45F⁡(\U0001D43B,\U0001D43E(\U0001D458)\r\n\U0001D45B)
    of \U0001D458-uniform hypergraphs, where \U0001D43B is a fixed linear \U0001D458-uniform
    hypergraph and \U0001D43E(\U0001D458)\r\n\U0001D45B is complete on \U0001D45B
    vertices. Recently, Conlon, Fox, Gunby, He, Mubayi, Suk, and Verstraëte disproved
    the folklore conjecture that \U0001D45F⁡(\U0001D43B,\U0001D43E(3)\r\n\U0001D45B)
    always grows polynomially in \U0001D45B. In this paper, we show that much larger
    growth rates are possible in higher uniformity. In uniformity \U0001D458 ≥4, we
    prove that for any constant \U0001D436 >0, there exists a linear \U0001D458-uniform
    hypergraph \U0001D43B for which\r\n\r\n\U0001D45F⁡(\U0001D43B,\U0001D43E(\U0001D458)\r\n\U0001D45B)≥twr\U0001D458−2⁢(2(log⁡\U0001D45B)\U0001D436)."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xiaoyu
  full_name: He, Xiaoyu
  last_name: He
- first_name: Jiaxi
  full_name: Nie, Jiaxi
  last_name: Nie
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
- first_name: Hung-Hsun
  full_name: Yu, Hung-Hsun
  last_name: Yu
citation:
  ama: He X, Nie J, Wigderson Y, Yu H-H. Off-diagonal Ramsey numbers for linear hypergraphs.
    <i>Combinatorics, Probability and Computing</i>. 2026:1-14. doi:<a href="https://doi.org/10.1017/s0963548326100443">10.1017/s0963548326100443</a>
  apa: He, X., Nie, J., Wigderson, Y., &#38; Yu, H.-H. (2026). Off-diagonal Ramsey
    numbers for linear hypergraphs. <i>Combinatorics, Probability and Computing</i>.
    Cambridge University Press. <a href="https://doi.org/10.1017/s0963548326100443">https://doi.org/10.1017/s0963548326100443</a>
  chicago: He, Xiaoyu, Jiaxi Nie, Yuval Wigderson, and Hung-Hsun Yu. “Off-Diagonal
    Ramsey Numbers for Linear Hypergraphs.” <i>Combinatorics, Probability and Computing</i>.
    Cambridge University Press, 2026. <a href="https://doi.org/10.1017/s0963548326100443">https://doi.org/10.1017/s0963548326100443</a>.
  ieee: X. He, J. Nie, Y. Wigderson, and H.-H. Yu, “Off-diagonal Ramsey numbers for
    linear hypergraphs,” <i>Combinatorics, Probability and Computing</i>. Cambridge
    University Press, pp. 1–14, 2026.
  ista: He X, Nie J, Wigderson Y, Yu H-H. 2026. Off-diagonal Ramsey numbers for linear
    hypergraphs. Combinatorics, Probability and Computing., 1–14.
  mla: He, Xiaoyu, et al. “Off-Diagonal Ramsey Numbers for Linear Hypergraphs.” <i>Combinatorics,
    Probability and Computing</i>, Cambridge University Press, 2026, pp. 1–14, doi:<a
    href="https://doi.org/10.1017/s0963548326100443">10.1017/s0963548326100443</a>.
  short: X. He, J. Nie, Y. Wigderson, H.-H. Yu, Combinatorics, Probability and Computing
    (2026) 1–14.
date_created: 2026-06-29T10:47:02Z
date_published: 2026-04-14T00:00:00Z
date_updated: 2026-07-08T07:24:54Z
day: '14'
ddc:
- '500'
doi: 10.1017/s0963548326100443
extern: '1'
external_id:
  arxiv:
  - '2507.05641'
fulldoi: https://doi.org/10.1017/s0963548326100443
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1017/S0963548326100443
mathsc:
- 05D10
- 05D40
- 05C65
month: '04'
oa: 1
oa_version: Published Version
page: 1-14
publication: Combinatorics, Probability and Computing
publication_identifier:
  eissn:
  - 1469-2163
  issn:
  - 0963-5483
publication_status: epub_ahead
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Off-diagonal Ramsey numbers for linear hypergraphs
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
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '22184'
abstract:
- lang: eng
  text: "Ramsey's theorem states that if N\r\n is sufficiently large, then no matter
    how one colors the edges among N\r\n vertices with two colors, there are always
    k\r\n vertices spanning edges in only one color. Given this theorem, it is natural
    to ask \"how large is sufficiently large?\" Ramsey's original proof showed that
    N=k!\r\n is sufficient, and five years later Erdős and Szekeres improved this
    bound to N=4^k\r\n. And then progress stalled for almost 90 years.\r\n\r\nIn this
    survey, I present the history of the problem, and discuss some of the ideas used
    in the recent breakthrough of Campos–Griffiths–Morris–Sahasrabudhe, who proved
    that N=3.993^k\r\n is sufficient. In addition, I discuss the subsequent work of
    Balister, Bollobás, Campos, Griffiths, Hurley, Morris, Sahasrabudhe, and Tiba,
    who gave an alternative, and more conceptual, proof."
- lang: fre
  text: "Le théorème de Ramsey stipule que si N\r\n est suffisamment grand, alors
    quelle que soit la manière dont l'on colore les arêtes entre N\r\n sommets avec
    deux couleurs, il y a toujours k\r\n sommets dont les arêtes ne sont colorées
    que d'une seule couleur. Compte tenu de ce théorème, il est naturel de se demander
    \"À quel point N\r\n doit être grand ?\" La preuve originale de Ramsey a montré
    que N=k!\r\n suffit, et cinq ans plus tard, Erdős et Szekeres ont amélioré cette
    borne à N=4k\r\n. Puis le progrès s'est arrêté pendant près de 90 ans.\r\n\r\nDans
    cet exposé, je présente l'histoire du problème et je discute certaines idées utilisées
    dans la percée récente de Campos--Griffiths-Morris--Sahasrabudhe, qui ont prouvé
    que N=3,993k\r\n suffit. De plus, je discute le travail suivant de Balister, Bollobás,
    Campos, Griffiths, Hurley, Morris, Sahasrabudhe, et Tiba, qui ont donné une preuve
    alternative et plus conceptuelle."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
citation:
  ama: 'Wigderson Y. Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey numbers
    (after Campos, Griffiths, Morris, and Sahasrabudhe). <i>Astérisque</i>. 2026:85-138.
    doi:<a href="https://doi.org/10.24033/ast.1255">10.24033/ast.1255</a>'
  apa: 'Wigderson, Y. (2026). Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey
    numbers (after Campos, Griffiths, Morris, and Sahasrabudhe). <i>Astérisque</i>.
    Societe Mathematique de France. <a href="https://doi.org/10.24033/ast.1255">https://doi.org/10.24033/ast.1255</a>'
  chicago: 'Wigderson, Yuval. “Exposé Bourbaki 1230 : Upper Bounds on Diagonal Ramsey
    Numbers (after Campos, Griffiths, Morris, and Sahasrabudhe).” <i>Astérisque</i>.
    Societe Mathematique de France, 2026. <a href="https://doi.org/10.24033/ast.1255">https://doi.org/10.24033/ast.1255</a>.'
  ieee: 'Y. Wigderson, “Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey numbers
    (after Campos, Griffiths, Morris, and Sahasrabudhe),” <i>Astérisque</i>. Societe
    Mathematique de France, pp. 85–138, 2026.'
  ista: 'Wigderson Y. 2026. Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey
    numbers (after Campos, Griffiths, Morris, and Sahasrabudhe). Astérisque., 85–138.'
  mla: 'Wigderson, Yuval. “Exposé Bourbaki 1230 : Upper Bounds on Diagonal Ramsey
    Numbers (after Campos, Griffiths, Morris, and Sahasrabudhe).” <i>Astérisque</i>,
    Societe Mathematique de France, 2026, pp. 85–138, doi:<a href="https://doi.org/10.24033/ast.1255">10.24033/ast.1255</a>.'
  short: Y. Wigderson, Astérisque (2026) 85–138.
date_created: 2026-06-29T12:02:59Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-07-14T09:53:07Z
day: '01'
doi: 10.24033/ast.1255
extern: '1'
external_id:
  arxiv:
  - '2411.09321'
fulldoi: https://doi.org/10.24033/ast.1255
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: 'https://doi.org/10.48550/arXiv.2411.09321 '
mathsc:
- 05D10
- 05C55
month: '01'
oa: 1
oa_version: Preprint
page: 85-138
publication: Astérisque
publication_identifier:
  issn:
  - 0303-1179
  - 2492-5926
publication_status: published
publisher: Societe Mathematique de France
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Exposé Bourbaki 1230 : Upper bounds on diagonal Ramsey numbers (after Campos,
  Griffiths, Morris, and Sahasrabudhe)'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '22155'
abstract:
- lang: eng
  text: "The canonical Ramsey theorem of Erdős and Rado implies that for any graph
    \U0001D43B, any edge-coloring (with an arbitrary number of colors) of a sufficiently
    large complete graph \U0001D43E\U0001D441 contains a monochromatic, lexicographic,
    or rainbow copy of \U0001D43B. The least such \U0001D441 is called the Erdős–Rado
    number of \U0001D43B, denoted by \U0001D438⁢\U0001D445⁡(\U0001D43B). Erdős–Rado
    numbers of cliques have received considerable attention, and in this paper we
    extend this line of research by studying Erdős–Rado numbers of sparse graphs.
    For example, we prove that if \U0001D43B has bounded degree, then \U0001D438⁢\U0001D445⁡(\U0001D43B)
    is polynomial in |\U0001D449⁡(\U0001D43B)| if \U0001D43B is bipartite but exponential
    in general. We also study the closely related problem of constrained Ramsey numbers.
    For a given tree S and given path \U0001D443\U0001D461, we study the minimum \U0001D441
    such that every edge-coloring of \U0001D43E\U0001D441 contains a monochromatic
    copy of S or a rainbow copy of \U0001D443\U0001D461. We prove a nearly optimal
    upper bound for this problem, which differs from the best known lower bound by
    a function of inverse Ackermann type."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lior
  full_name: Gishboliner, Lior
  last_name: Gishboliner
- first_name: Aleksa
  full_name: Milojević, Aleksa
  last_name: Milojević
- first_name: Benny
  full_name: Sudakov, Benny
  last_name: Sudakov
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
citation:
  ama: Gishboliner L, Milojević A, Sudakov B, Wigderson Y. Canonical Ramsey numbers
    of sparse graphs. <i>SIAM Journal on Discrete Mathematics</i>. 2025;39(3):1491-1519.
    doi:<a href="https://doi.org/10.1137/24m1714964">10.1137/24m1714964</a>
  apa: Gishboliner, L., Milojević, A., Sudakov, B., &#38; Wigderson, Y. (2025). Canonical
    Ramsey numbers of sparse graphs. <i>SIAM Journal on Discrete Mathematics</i>.
    Society for Industrial &#38; Applied Mathematics. <a href="https://doi.org/10.1137/24m1714964">https://doi.org/10.1137/24m1714964</a>
  chicago: Gishboliner, Lior, Aleksa Milojević, Benny Sudakov, and Yuval Wigderson.
    “Canonical Ramsey Numbers of Sparse Graphs.” <i>SIAM Journal on Discrete Mathematics</i>.
    Society for Industrial &#38; Applied Mathematics, 2025. <a href="https://doi.org/10.1137/24m1714964">https://doi.org/10.1137/24m1714964</a>.
  ieee: L. Gishboliner, A. Milojević, B. Sudakov, and Y. Wigderson, “Canonical Ramsey
    numbers of sparse graphs,” <i>SIAM Journal on Discrete Mathematics</i>, vol. 39,
    no. 3. Society for Industrial &#38; Applied Mathematics, pp. 1491–1519, 2025.
  ista: Gishboliner L, Milojević A, Sudakov B, Wigderson Y. 2025. Canonical Ramsey
    numbers of sparse graphs. SIAM Journal on Discrete Mathematics. 39(3), 1491–1519.
  mla: Gishboliner, Lior, et al. “Canonical Ramsey Numbers of Sparse Graphs.” <i>SIAM
    Journal on Discrete Mathematics</i>, vol. 39, no. 3, Society for Industrial &#38;
    Applied Mathematics, 2025, pp. 1491–519, doi:<a href="https://doi.org/10.1137/24m1714964">10.1137/24m1714964</a>.
  short: L. Gishboliner, A. Milojević, B. Sudakov, Y. Wigderson, SIAM Journal on Discrete
    Mathematics 39 (2025) 1491–1519.
date_created: 2026-06-29T10:49:48Z
date_published: 2025-09-01T00:00:00Z
date_updated: 2026-07-08T07:38:44Z
day: '01'
doi: 10.1137/24m1714964
extern: '1'
external_id:
  arxiv:
  - '2410.08644'
fulldoi: https://doi.org/10.1137/24m1714964
intvolume: '        39'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2410.08644
mathsc:
- 05D10
month: '09'
oa: 1
oa_version: Preprint
page: 1491-1519
publication: SIAM Journal on Discrete Mathematics
publication_identifier:
  eissn:
  - 1095-7146
  issn:
  - 0895-4801
publication_status: published
publisher: Society for Industrial & Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Canonical Ramsey numbers of sparse graphs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 39
year: '2025'
...
---
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'
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'
...
---
OA_place: repository
OA_type: green
_id: '22168'
abstract:
- lang: eng
  text: "Let us say that a graph G is Ramsey for a tuple (H1, ... , Hr) of graphs
    if every r-colouring\r\nof the edges of G contains a monochromatic copy of Hi
    in colour i, for some i ∈ [[r]].\r\nA famous conjecture of Kohayakawa and Kreuter,
    extending seminal work of Rödl and\r\nRucinski, predicts the threshold at which
    the binomial random graph ´ Gn,p becomes Ramsey\r\nfor (H1, ... , Hr) asymptotically
    almost surely.\r\nIn this paper, we resolve the Kohayakawa–Kreuter conjecture
    for almost all tuples of\r\ngraphs. Moreover, we reduce its validity to the truth
    of a certain deterministic statement,\r\nwhich is a clear necessary condition
    for the conjecture to hold. All of our results actually hold in greater generality,
    when one replaces the graphs H1, ... , Hr by finite families\r\nH1, ... , Hr.
    Additionally, we pose a natural (deterministic) graph-partitioning conjecture,\r\nwhich
    we believe to be of independent interest, and whose resolution would imply the\r\nKohayakawa–Kreuter
    conjecture."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: EDEN
  full_name: KUPERWASSER, EDEN
  last_name: KUPERWASSER
- first_name: WOJCIECH
  full_name: SAMOTIJ, WOJCIECH
  last_name: SAMOTIJ
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
citation:
  ama: KUPERWASSER E, SAMOTIJ W, Wigderson Y. On the Kohayakawa–Kreuter conjecture.
    <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2025;178(3):293-320.
    doi:<a href="https://doi.org/10.1017/s0305004125000143">10.1017/s0305004125000143</a>
  apa: KUPERWASSER, E., SAMOTIJ, W., &#38; Wigderson, Y. (2025). On the Kohayakawa–Kreuter
    conjecture. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>.
    Cambridge University Press. <a href="https://doi.org/10.1017/s0305004125000143">https://doi.org/10.1017/s0305004125000143</a>
  chicago: KUPERWASSER, EDEN, WOJCIECH SAMOTIJ, and Yuval Wigderson. “On the Kohayakawa–Kreuter
    Conjecture.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>.
    Cambridge University Press, 2025. <a href="https://doi.org/10.1017/s0305004125000143">https://doi.org/10.1017/s0305004125000143</a>.
  ieee: E. KUPERWASSER, W. SAMOTIJ, and Y. Wigderson, “On the Kohayakawa–Kreuter conjecture,”
    <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 178,
    no. 3. Cambridge University Press, pp. 293–320, 2025.
  ista: KUPERWASSER E, SAMOTIJ W, Wigderson Y. 2025. On the Kohayakawa–Kreuter conjecture.
    Mathematical Proceedings of the Cambridge Philosophical Society. 178(3), 293–320.
  mla: KUPERWASSER, EDEN, et al. “On the Kohayakawa–Kreuter Conjecture.” <i>Mathematical
    Proceedings of the Cambridge Philosophical Society</i>, vol. 178, no. 3, Cambridge
    University Press, 2025, pp. 293–320, doi:<a href="https://doi.org/10.1017/s0305004125000143">10.1017/s0305004125000143</a>.
  short: E. KUPERWASSER, W. SAMOTIJ, Y. Wigderson, Mathematical Proceedings of the
    Cambridge Philosophical Society 178 (2025) 293–320.
date_created: 2026-06-29T10:55:00Z
date_published: 2025-04-28T00:00:00Z
date_updated: 2026-07-14T08:38:08Z
day: '28'
doi: 10.1017/s0305004125000143
extern: '1'
external_id:
  arxiv:
  - '2307.16611'
fulldoi: https://doi.org/10.1017/s0305004125000143
intvolume: '       178'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2307.16611
mathsc:
- 05C80
- 05C55
- 05D10
month: '04'
oa: 1
oa_version: Preprint
page: 293-320
publication: Mathematical Proceedings of the Cambridge Philosophical Society
publication_identifier:
  eissn:
  - 1469-8064
  issn:
  - 0305-0041
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the Kohayakawa–Kreuter conjecture
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 178
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22165'
abstract:
- lang: eng
  text: "The book graph \U0001D435(\U0001D458)\r\n\U0001D45B consists of \U0001D45B
    copies of \U0001D43E\U0001D458+1 joined along a common \U0001D43E\U0001D458. In
    the prequel to this paper, we studied the diagonal Ramsey number \U0001D45F⁡(\U0001D435(\U0001D458)\r\n\U0001D45B,\U0001D435(\U0001D458)\r\n\U0001D45B).
    Here we consider the natural off-diagonal variant \U0001D45F⁡(\U0001D435(\U0001D458)\r\n\U0001D450⁢\U0001D45B,\U0001D435(\U0001D458)\r\n\U0001D45B)
    for fixed \U0001D450 ∈(0,1]. In this more general setting, we show that an interesting
    dichotomy emerges: for very small \U0001D450, a simple \U0001D458-partite construction
    dictates the Ramsey function and all nearly-extremal colourings are close to being
    \U0001D458-partite, while, for \U0001D450 bounded away from 0, random colourings
    of an appropriate density are asymptotically optimal and all nearly-extremal colourings
    are quasirandom. Our investigations also open up a range of questions about what
    happens for intermediate values of \U0001D450.\r\n\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: David
  full_name: Conlon, David
  last_name: Conlon
- first_name: Jacob
  full_name: Fox, Jacob
  last_name: Fox
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
citation:
  ama: Conlon D, Fox J, Wigderson Y. Off-diagonal book Ramsey numbers. <i>Combinatorics,
    Probability and Computing</i>. 2023;32(3):516-545. doi:<a href="https://doi.org/10.1017/s0963548322000360">10.1017/s0963548322000360</a>
  apa: Conlon, D., Fox, J., &#38; Wigderson, Y. (2023). Off-diagonal book Ramsey numbers.
    <i>Combinatorics, Probability and Computing</i>. Cambridge University Press. <a
    href="https://doi.org/10.1017/s0963548322000360">https://doi.org/10.1017/s0963548322000360</a>
  chicago: Conlon, David, Jacob Fox, and Yuval Wigderson. “Off-Diagonal Book Ramsey
    Numbers.” <i>Combinatorics, Probability and Computing</i>. Cambridge University
    Press, 2023. <a href="https://doi.org/10.1017/s0963548322000360">https://doi.org/10.1017/s0963548322000360</a>.
  ieee: D. Conlon, J. Fox, and Y. Wigderson, “Off-diagonal book Ramsey numbers,” <i>Combinatorics,
    Probability and Computing</i>, vol. 32, no. 3. Cambridge University Press, pp.
    516–545, 2023.
  ista: Conlon D, Fox J, Wigderson Y. 2023. Off-diagonal book Ramsey numbers. Combinatorics,
    Probability and Computing. 32(3), 516–545.
  mla: Conlon, David, et al. “Off-Diagonal Book Ramsey Numbers.” <i>Combinatorics,
    Probability and Computing</i>, vol. 32, no. 3, Cambridge University Press, 2023,
    pp. 516–45, doi:<a href="https://doi.org/10.1017/s0963548322000360">10.1017/s0963548322000360</a>.
  short: D. Conlon, J. Fox, Y. Wigderson, Combinatorics, Probability and Computing
    32 (2023) 516–545.
date_created: 2026-06-29T10:53:47Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2026-07-14T08:27:40Z
day: '01'
doi: 10.1017/s0963548322000360
extern: '1'
external_id:
  arxiv:
  - '2110.14483'
fulldoi: https://doi.org/10.1017/s0963548322000360
intvolume: '        32'
issue: '3'
keyword:
- Ramsey theory
- book graphs
- Ramsey goodness
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2110.14483
mathsc:
- 05C55
- 05D10
month: '05'
oa: 1
oa_version: Preprint
page: 516-545
publication: Combinatorics, Probability and Computing
publication_identifier:
  eissn:
  - 1469-2163
  issn:
  - 0963-5483
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Off-diagonal book Ramsey numbers
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 32
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '22182'
abstract:
- lang: eng
  text: We present a short new proof of the canonical polynomial van der Waerden theorem,
    recently established by Girão.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jacob
  full_name: Fox, Jacob
  last_name: Fox
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
- first_name: Yufei
  full_name: Zhao, Yufei
  last_name: Zhao
citation:
  ama: Fox J, Wigderson Y, Zhao Y. A short proof of the canonical polynomial van der
    Waerden theorem. <i>Comptes Rendus Mathématique</i>. 2020;358(8):957-959. doi:<a
    href="https://doi.org/10.5802/crmath.101">10.5802/crmath.101</a>
  apa: Fox, J., Wigderson, Y., &#38; Zhao, Y. (2020). A short proof of the canonical
    polynomial van der Waerden theorem. <i>Comptes Rendus Mathématique</i>. Académie
    des Sciences. <a href="https://doi.org/10.5802/crmath.101">https://doi.org/10.5802/crmath.101</a>
  chicago: Fox, Jacob, Yuval Wigderson, and Yufei Zhao. “A Short Proof of the Canonical
    Polynomial van Der Waerden Theorem.” <i>Comptes Rendus Mathématique</i>. Académie
    des Sciences, 2020. <a href="https://doi.org/10.5802/crmath.101">https://doi.org/10.5802/crmath.101</a>.
  ieee: J. Fox, Y. Wigderson, and Y. Zhao, “A short proof of the canonical polynomial
    van der Waerden theorem,” <i>Comptes Rendus Mathématique</i>, vol. 358, no. 8.
    Académie des Sciences, pp. 957–959, 2020.
  ista: Fox J, Wigderson Y, Zhao Y. 2020. A short proof of the canonical polynomial
    van der Waerden theorem. Comptes Rendus Mathématique. 358(8), 957–959.
  mla: Fox, Jacob, et al. “A Short Proof of the Canonical Polynomial van Der Waerden
    Theorem.” <i>Comptes Rendus Mathématique</i>, vol. 358, no. 8, Académie des Sciences,
    2020, pp. 957–59, doi:<a href="https://doi.org/10.5802/crmath.101">10.5802/crmath.101</a>.
  short: J. Fox, Y. Wigderson, Y. Zhao, Comptes Rendus Mathématique 358 (2020) 957–959.
date_created: 2026-06-29T11:00:09Z
date_published: 2020-12-03T00:00:00Z
date_updated: 2026-07-14T09:19:20Z
day: '03'
doi: 10.5802/crmath.101
extern: '1'
external_id:
  arxiv:
  - '2005.04135'
fulldoi: https://doi.org/10.5802/crmath.101
intvolume: '       358'
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2005.04135
mathsc:
- 05D10
- 11B30
month: '12'
oa: 1
oa_version: Preprint
page: 957-959
publication: Comptes Rendus Mathématique
publication_identifier:
  eissn:
  - 1778-3569
  issn:
  - 1631-073X
publication_status: published
publisher: Académie des Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: A short proof of the canonical polynomial van der Waerden theorem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 358
year: '2020'
...
---
OA_place: repository
OA_type: green
_id: '22185'
abstract:
- lang: eng
  text: "A weakly optimal Ks-free (n,d,λ)-graph is ad-regular Ks-free graph on n vertices
    with d= Θ(n1−α) and spectral expansion λ= Θ(n1−(s−1)α),  for some fixed α >0.
    \ Such a graph is called optimal if additionally α=12s−3.  We prove that if s1,...,sk>3
    are fixed positive integers and weakly optimal Ksi-free pseudorandom graphs exist
    for each 1<i<k, then the multicolor Ramsey numbers satisfy \r\n\r\nΩ(tS+1log2St)6r(s1,...,sk,t)6O(tS+1logSt),\r\nas
    t→∞, where S=∑ki=1(si−2). This generalizes previous results of Mubayi andVerstraete,
    who proved the case k= 1, and Alon and Rodl, who proved the cases1=···=sk= 3.
    \ Both previous results used the existence of optimal rather than weakly optimal
    Ksi-free graphs"
article_number: P1.32
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xiaoyu
  full_name: He, Xiaoyu
  last_name: He
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
citation:
  ama: He X, Wigderson Y. Multicolor Ramsey numbers via pseudorandom graphs. <i>The
    Electronic Journal of Combinatorics</i>. 2020;27(1). doi:<a href="https://doi.org/10.37236/9071">10.37236/9071</a>
  apa: He, X., &#38; Wigderson, Y. (2020). Multicolor Ramsey numbers via pseudorandom
    graphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal
    of Combinatorics. <a href="https://doi.org/10.37236/9071">https://doi.org/10.37236/9071</a>
  chicago: He, Xiaoyu, and Yuval Wigderson. “Multicolor Ramsey Numbers via Pseudorandom
    Graphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal
    of Combinatorics, 2020. <a href="https://doi.org/10.37236/9071">https://doi.org/10.37236/9071</a>.
  ieee: X. He and Y. Wigderson, “Multicolor Ramsey numbers via pseudorandom graphs,”
    <i>The Electronic Journal of Combinatorics</i>, vol. 27, no. 1. The Electronic
    Journal of Combinatorics, 2020.
  ista: He X, Wigderson Y. 2020. Multicolor Ramsey numbers via pseudorandom graphs.
    The Electronic Journal of Combinatorics. 27(1), P1.32.
  mla: He, Xiaoyu, and Yuval Wigderson. “Multicolor Ramsey Numbers via Pseudorandom
    Graphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 27, no. 1, P1.32,
    The Electronic Journal of Combinatorics, 2020, doi:<a href="https://doi.org/10.37236/9071">10.37236/9071</a>.
  short: X. He, Y. Wigderson, The Electronic Journal of Combinatorics 27 (2020).
date_created: 2026-06-29T12:06:14Z
date_published: 2020-02-01T00:00:00Z
date_updated: 2026-07-14T09:42:53Z
day: '01'
doi: 10.37236/9071
extern: '1'
external_id:
  arxiv:
  - '1910.06287'
fulldoi: https://doi.org/10.37236/9071
intvolume: '        27'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1910.06287
mathsc:
- 05C55
- 05D10
month: '02'
oa: 1
oa_version: Preprint
publication: The Electronic Journal of Combinatorics
publication_identifier:
  eissn:
  - 1077-8926
publication_status: published
publisher: The Electronic Journal of Combinatorics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multicolor Ramsey numbers via pseudorandom graphs
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 27
year: '2020'
...