[{"publisher":"American Mathematical Society","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."}],"quality_controlled":"1","title":"Ordered Ramsey numbers of graphs with 𝑚 edges","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2412.17599"}],"publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"date_updated":"2026-07-14T08:34:43Z","status":"public","doi":"10.1090/proc/17442","arxiv":1,"oa":1,"article_type":"original","date_published":"2026-01-16T00:00:00Z","external_id":{"arxiv":["2412.17599"]},"_id":"22167","date_created":"2026-06-29T10:54:32Z","year":"2026","article_processing_charge":"No","day":"16","publication":"Proceedings of the American Mathematical Society","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","OA_type":"green","issue":"3","citation":{"ieee":"D. Bradač, P. Morawski, B. Sudakov, and Y. Wigderson, “Ordered Ramsey numbers of graphs with 𝑚 edges,” <i>Proceedings of the American Mathematical Society</i>, vol. 154, no. 3. American Mathematical Society, pp. 927–942, 2026.","chicago":"Bradač, Domagoj, Patryk Morawski, Benny Sudakov, and Yuval Wigderson. “Ordered Ramsey Numbers of Graphs with 𝑚 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>.","mla":"Bradač, Domagoj, et al. “Ordered Ramsey Numbers of Graphs with 𝑚 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>.","ista":"Bradač D, Morawski P, Sudakov B, Wigderson Y. 2026. Ordered Ramsey numbers of graphs with 𝑚 edges. Proceedings of the American Mathematical Society. 154(3), 927–942.","ama":"Bradač D, Morawski P, Sudakov B, Wigderson Y. Ordered Ramsey numbers of graphs with 𝑚 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 𝑚 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>","short":"D. Bradač, P. Morawski, B. Sudakov, Y. Wigderson, Proceedings of the American Mathematical Society 154 (2026) 927–942."},"OA_place":"repository","extern":"1","page":"927-942","oa_version":"Preprint","language":[{"iso":"eng"}],"intvolume":"       154","scopus_import":"1","volume":154,"month":"01","publication_status":"published","author":[{"full_name":"Bradač, Domagoj","last_name":"Bradač","first_name":"Domagoj"},{"first_name":"Patryk","full_name":"Morawski, Patryk","last_name":"Morawski"},{"first_name":"Benny","full_name":"Sudakov, Benny","last_name":"Sudakov"},{"first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson","full_name":"Wigderson, Yuval"}]}]