---
OA_place: repository
OA_type: green
_id: '22174'
abstract:
- lang: eng
  text: "The book graph B\r\n(k)\r\nn consists of n copies of Kk+1 joined along a
    common Kk. The Ramsey\r\nnumbers of B\r\n(k)\r\nn are known to have strong connections
    to the classical Ramsey numbers\r\nof cliques. Recently, the first author determined
    the asymptotic order of these Ramsey\r\nnumbers for fixed k, thus answering an
    old question of Erd˝os, Faudree, Rousseau, and\r\nSchelp. In this paper, we first
    provide a simpler proof of this theorem. Next, answering a\r\nquestion of the
    first author, we present a different proof that avoids the use of Szemer´edi’s\r\nregularity
    lemma, thus providing much tighter control on the error term. Finally, we prove\r\na
    conjecture of Nikiforov, Rousseau, and Schelp by showing that all extremal colorings
    for\r\nthis Ramsey problem are quasirandom"
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. Ramsey numbers of books and quasirandomness.
    <i>Combinatorica</i>. 2022;42(3):309-363. doi:<a href="https://doi.org/10.1007/s00493-021-4409-9">10.1007/s00493-021-4409-9</a>
  apa: Conlon, D., Fox, J., &#38; Wigderson, Y. (2022). Ramsey numbers of books and
    quasirandomness. <i>Combinatorica</i>. Springer Nature. <a href="https://doi.org/10.1007/s00493-021-4409-9">https://doi.org/10.1007/s00493-021-4409-9</a>
  chicago: Conlon, David, Jacob Fox, and Yuval Wigderson. “Ramsey Numbers of Books
    and Quasirandomness.” <i>Combinatorica</i>. Springer Nature, 2022. <a href="https://doi.org/10.1007/s00493-021-4409-9">https://doi.org/10.1007/s00493-021-4409-9</a>.
  ieee: D. Conlon, J. Fox, and Y. Wigderson, “Ramsey numbers of books and quasirandomness,”
    <i>Combinatorica</i>, vol. 42, no. 3. Springer Nature, pp. 309–363, 2022.
  ista: Conlon D, Fox J, Wigderson Y. 2022. Ramsey numbers of books and quasirandomness.
    Combinatorica. 42(3), 309–363.
  mla: Conlon, David, et al. “Ramsey Numbers of Books and Quasirandomness.” <i>Combinatorica</i>,
    vol. 42, no. 3, Springer Nature, 2022, pp. 309–63, doi:<a href="https://doi.org/10.1007/s00493-021-4409-9">10.1007/s00493-021-4409-9</a>.
  short: D. Conlon, J. Fox, Y. Wigderson, Combinatorica 42 (2022) 309–363.
date_created: 2026-06-29T10:57:27Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2026-07-14T08:57:12Z
day: '01'
doi: 10.1007/s00493-021-4409-9
extern: '1'
external_id:
  arxiv:
  - '2001.00407'
intvolume: '        42'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2001.00407
month: '06'
oa: 1
oa_version: Preprint
page: 309-363
publication: Combinatorica
publication_identifier:
  eissn:
  - 1439-6912
  issn:
  - 0209-9683
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ramsey numbers of books and quasirandomness
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 42
year: '2022'
...