{"publisher":"Alliance of Diamond Open Access Journals","arxiv":1,"doi":"10.19086/aic.2023.2","OA_type":"green","day":"01","scopus_import":"1","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2026-06-29T10:55:46Z","OA_place":"repository","language":[{"iso":"eng"}],"external_id":{"arxiv":["2207.07775"]},"year":"2023","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2207.07775","open_access":"1"}],"article_processing_charge":"No","citation":{"short":"J. Fox, Y. Wigderson, Advances in Combinatorics (2023).","ista":"Fox J, Wigderson Y. 2023. Ramsey multiplicity and the Turán coloring. Advances in Combinatorics.","chicago":"Fox, Jacob, and Yuval Wigderson. “Ramsey Multiplicity and the Turán Coloring.” <i>Advances in Combinatorics</i>. Alliance of Diamond Open Access Journals, 2023. <a href=\"https://doi.org/10.19086/aic.2023.2\">https://doi.org/10.19086/aic.2023.2</a>.","ieee":"J. Fox and Y. Wigderson, “Ramsey multiplicity and the Turán coloring,” <i>Advances in Combinatorics</i>. Alliance of Diamond Open Access Journals, 2023.","mla":"Fox, Jacob, and Yuval Wigderson. “Ramsey Multiplicity and the Turán Coloring.” <i>Advances in Combinatorics</i>, Alliance of Diamond Open Access Journals, 2023, doi:<a href=\"https://doi.org/10.19086/aic.2023.2\">10.19086/aic.2023.2</a>.","ama":"Fox J, Wigderson Y. Ramsey multiplicity and the Turán coloring. <i>Advances in Combinatorics</i>. 2023. doi:<a href=\"https://doi.org/10.19086/aic.2023.2\">10.19086/aic.2023.2</a>","apa":"Fox, J., &#38; Wigderson, Y. (2023). Ramsey multiplicity and the Turán coloring. <i>Advances in Combinatorics</i>. Alliance of Diamond Open Access Journals. <a href=\"https://doi.org/10.19086/aic.2023.2\">https://doi.org/10.19086/aic.2023.2</a>"},"type":"journal_article","publication_identifier":{"eissn":["2517-5599"]},"status":"public","_id":"22170","month":"01","abstract":[{"lang":"eng","text":"Extending an earlier conjecture of Erdős, Burr and Rosta conjectured that among all two-colorings of the edges of a complete graph, the uniformly random coloring asymptotically minimizes the number of monochromatic copies of any fixed graph H. This conjecture was disproved independently by Sidorenko and Thomason. The first author later found quantitatively stronger counterexamples, using the Turán coloring, in which one of the two colors spans a balanced complete multipartite graph.\r\nWe prove that the Turán coloring is extremal for an infinite family of graphs, and that it is the unique extremal coloring. This yields the first determination of the Ramsey multiplicity constant of a graph for which the Burr--Rosta conjecture fails.\r\nWe also prove an analogous three-color result. In this case, our result is conditional on a certain natural conjecture on the behavior of two-color Ramsey numbers."}],"date_updated":"2026-07-14T08:45:53Z","article_type":"original","oa_version":"Preprint","title":"Ramsey multiplicity and the Turán coloring","date_published":"2023-01-01T00:00:00Z","author":[{"last_name":"Fox","full_name":"Fox, Jacob","first_name":"Jacob"},{"first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","full_name":"Wigderson, Yuval","last_name":"Wigderson"}],"publication_status":"published","publication":"Advances in Combinatorics","extern":"1","quality_controlled":"1"}