[{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","oa_version":"Preprint","volume":130,"date_published":"2025-01-01T00:00:00Z","article_processing_charge":"No","title":"Resolution of the Kohayakawa–Kreuter conjecture","author":[{"full_name":"Christoph, Micha","first_name":"Micha","last_name":"Christoph"},{"last_name":"Martinsson","full_name":"Martinsson, Anders","first_name":"Anders"},{"first_name":"Raphael","full_name":"Steiner, Raphael","last_name":"Steiner"},{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson","first_name":"Yuval","full_name":"Wigderson, Yuval"}],"external_id":{"arxiv":["2402.03045"]},"article_number":"e70013","ddc":["500"],"publication_identifier":{"eissn":["1460-244X"],"issn":["0024-6115"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2402.03045","open_access":"1"}],"month":"01","intvolume":"       130","status":"public","arxiv":1,"publisher":"Wiley","OA_place":"repository","publication":"Proceedings of the London Mathematical Society","article_type":"original","mathsc":["05C70","05D10","05C80"],"day":"01","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","date_created":"2026-06-29T10:50:35Z","publication_status":"published","doi":"10.1112/plms.70013","extern":"1","quality_controlled":"1","citation":{"mla":"Christoph, Micha, et al. “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1, e70013, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/plms.70013\">10.1112/plms.70013</a>.","ieee":"M. Christoph, A. Martinsson, R. Steiner, and Y. Wigderson, “Resolution of the Kohayakawa–Kreuter conjecture,” <i>Proceedings of the London Mathematical Society</i>, vol. 130, no. 1. Wiley, 2025.","chicago":"Christoph, Micha, Anders Martinsson, Raphael Steiner, and Yuval Wigderson. “Resolution of the Kohayakawa–Kreuter Conjecture.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/plms.70013\">https://doi.org/10.1112/plms.70013</a>.","short":"M. Christoph, A. Martinsson, R. Steiner, Y. Wigderson, Proceedings of the London Mathematical Society 130 (2025).","ista":"Christoph M, Martinsson A, Steiner R, Wigderson Y. 2025. Resolution of the Kohayakawa–Kreuter conjecture. Proceedings of the London Mathematical Society. 130(1), e70013.","apa":"Christoph, M., Martinsson, A., Steiner, R., &#38; Wigderson, Y. (2025). Resolution of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70013\">https://doi.org/10.1112/plms.70013</a>","ama":"Christoph M, Martinsson A, Steiner R, Wigderson Y. Resolution of the Kohayakawa–Kreuter conjecture. <i>Proceedings of the London Mathematical Society</i>. 2025;130(1). doi:<a href=\"https://doi.org/10.1112/plms.70013\">10.1112/plms.70013</a>"},"date_updated":"2026-07-08T10:24:21Z","issue":"1","_id":"22157","scopus_import":"1","OA_type":"green","language":[{"iso":"eng"}],"oa":1,"abstract":[{"text":"A graph 𝐺 is said to be Ramsey for a tuple of graphs(𝐻 1 , … , 𝐻𝑟 ) if every 𝑟-coloring of the edges of 𝐺 con-tains a monochromatic copy of 𝐻𝑖 in color 𝑖, for some 𝑖.A fundamental question at the intersection of Ramseytheory and the theory of random graphs is to deter-mine the threshold at which the binomial randomgraph 𝐺𝑛,𝑝 becomes asymptotically almost surely Ram-sey for a fixed tuple (𝐻 1 , … , 𝐻𝑟 ), and a famous conjectureof Kohayakawa and Kreuter predicts this threshold.Earlier work of Mousset–Nenadov–Samotij, Bowtell–Hancock–Hyde, and Kuperwasser–Samotij–Wigdersonhas reduced this probabilistic problem to a determinis-tic graph decomposition conjecture. In this paper, weresolve this deterministic problem, thus proving theKohayakawa–Kreuter conjecture. Along the way, weprove a number of novel graph decomposition resultsthat may be of independent interest.","lang":"eng"}]}]