@article{22167,
  abstract     = {Given a vertex-ordered graph G, the ordered Ramsey number
r<(G) is the minimum integer N such that every 2-coloring of the edges of
the complete ordered graph KN contains a monochromatic ordered copy of G.
Motivated by a similar question posed by Erd˝os and Graham [On partition
theorems for finite graphs, Infinite and finite sets (Colloq., Keszthely, 1973),
North-Holland, Amsterdam-London, pp. 515–527] in the unordered setting,
we 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) ≤
e109√m(log log m)3/2
for any such G, which is tight up to the (log log m)3/2
factor in the exponent. As a corollary, we obtain the corresponding bound for
the oriented Ramsey number of a directed graph with m edges.},
  author       = {Bradač, Domagoj and Morawski, Patryk and Sudakov, Benny and Wigderson, Yuval},
  issn         = {1088-6826},
  journal      = {Proceedings of the American Mathematical Society},
  number       = {3},
  pages        = {927--942},
  publisher    = {American Mathematical Society},
  title        = {{Ordered Ramsey numbers of graphs with 𝑚 edges}},
  doi          = {10.1090/proc/17442},
  volume       = {154},
  year         = {2026},
}