---
OA_place: repository
OA_type: green
_id: '22167'
abstract:
- lang: eng
  text: "Given a vertex-ordered graph G, the ordered Ramsey number\r\nr<(G) is the
    minimum integer N such that every 2-coloring of the edges of\r\nthe complete ordered
    graph KN contains a monochromatic ordered copy of G.\r\nMotivated by a similar
    question posed by Erd˝os and Graham [On partition\r\ntheorems for finite graphs,
    Infinite and finite sets (Colloq., Keszthely, 1973),\r\nNorth-Holland, Amsterdam-London,
    pp. 515–527] in the unordered setting,\r\nwe study the problem of bounding the
    ordered Ramsey number of any ordered graph G with m edges and no isolated vertices.
    We prove that r<(G) ≤\r\ne109√m(log log m)3/2\r\nfor any such G, which is tight
    up to the (log log m)3/2\r\nfactor in the exponent. As a corollary, we obtain
    the corresponding bound for\r\nthe oriented Ramsey number of a directed graph
    with m edges."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Domagoj
  full_name: Bradač, Domagoj
  last_name: Bradač
- first_name: Patryk
  full_name: Morawski, Patryk
  last_name: Morawski
- 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: "Bradač D, Morawski P, Sudakov B, Wigderson Y. Ordered Ramsey numbers of graphs
    with \U0001D45A edges. <i>Proceedings of the American Mathematical Society</i>.
    2026;154(3):927-942. doi:<a href=\"https://doi.org/10.1090/proc/17442\">10.1090/proc/17442</a>"
  apa: "Bradač, D., Morawski, P., Sudakov, B., &#38; Wigderson, Y. (2026). Ordered
    Ramsey numbers of graphs with \U0001D45A edges. <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/17442\">https://doi.org/10.1090/proc/17442</a>"
  chicago: "Bradač, Domagoj, Patryk Morawski, Benny Sudakov, and Yuval Wigderson.
    “Ordered Ramsey Numbers of Graphs with \U0001D45A Edges.” <i>Proceedings of the
    American Mathematical Society</i>. American Mathematical Society, 2026. <a href=\"https://doi.org/10.1090/proc/17442\">https://doi.org/10.1090/proc/17442</a>."
  ieee: "D. Bradač, P. Morawski, B. Sudakov, and Y. Wigderson, “Ordered Ramsey numbers
    of graphs with \U0001D45A edges,” <i>Proceedings of the American Mathematical
    Society</i>, vol. 154, no. 3. American Mathematical Society, pp. 927–942, 2026."
  ista: "Bradač D, Morawski P, Sudakov B, Wigderson Y. 2026. Ordered Ramsey numbers
    of graphs with \U0001D45A edges. Proceedings of the American Mathematical Society.
    154(3), 927–942."
  mla: "Bradač, Domagoj, et al. “Ordered Ramsey Numbers of Graphs with \U0001D45A
    Edges.” <i>Proceedings of the American Mathematical Society</i>, vol. 154, no.
    3, American Mathematical Society, 2026, pp. 927–42, doi:<a href=\"https://doi.org/10.1090/proc/17442\">10.1090/proc/17442</a>."
  short: D. Bradač, P. Morawski, B. Sudakov, Y. Wigderson, Proceedings of the American
    Mathematical Society 154 (2026) 927–942.
date_created: 2026-06-29T10:54:32Z
date_published: 2026-01-16T00:00:00Z
date_updated: 2026-07-14T08:34:43Z
day: '16'
doi: 10.1090/proc/17442
extern: '1'
external_id:
  arxiv:
  - '2412.17599'
intvolume: '       154'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2412.17599
month: '01'
oa: 1
oa_version: Preprint
page: 927-942
publication: Proceedings of the American Mathematical Society
publication_identifier:
  eissn:
  - 1088-6826
  issn:
  - 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: "Ordered Ramsey numbers of graphs with \U0001D45A edges"
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 154
year: '2026'
...