---
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'
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'
...