{"date_published":"2025-04-28T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2026-06-29T10:55:00Z","publisher":"Cambridge University Press","type":"journal_article","article_type":"original","year":"2025","issue":"3","_id":"22168","oa_version":"Preprint","doi":"10.1017/s0305004125000143","mathsc":["05C80","05C55","05D10"],"extern":"1","date_updated":"2026-07-14T08:38:08Z","external_id":{"arxiv":["2307.16611"]},"article_processing_charge":"No","citation":{"chicago":"KUPERWASSER, EDEN, WOJCIECH SAMOTIJ, and Yuval Wigderson. “On the Kohayakawa–Kreuter Conjecture.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. Cambridge University Press, 2025. <a href=\"https://doi.org/10.1017/s0305004125000143\">https://doi.org/10.1017/s0305004125000143</a>.","ista":"KUPERWASSER E, SAMOTIJ W, Wigderson Y. 2025. On the Kohayakawa–Kreuter conjecture. Mathematical Proceedings of the Cambridge Philosophical Society. 178(3), 293–320.","apa":"KUPERWASSER, E., SAMOTIJ, W., &#38; Wigderson, Y. (2025). On the Kohayakawa–Kreuter conjecture. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/s0305004125000143\">https://doi.org/10.1017/s0305004125000143</a>","ama":"KUPERWASSER E, SAMOTIJ W, Wigderson Y. On the Kohayakawa–Kreuter conjecture. <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>. 2025;178(3):293-320. doi:<a href=\"https://doi.org/10.1017/s0305004125000143\">10.1017/s0305004125000143</a>","short":"E. KUPERWASSER, W. SAMOTIJ, Y. Wigderson, Mathematical Proceedings of the Cambridge Philosophical Society 178 (2025) 293–320.","mla":"KUPERWASSER, EDEN, et al. “On the Kohayakawa–Kreuter Conjecture.” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 178, no. 3, Cambridge University Press, 2025, pp. 293–320, doi:<a href=\"https://doi.org/10.1017/s0305004125000143\">10.1017/s0305004125000143</a>.","ieee":"E. KUPERWASSER, W. SAMOTIJ, and Y. Wigderson, “On the Kohayakawa–Kreuter conjecture,” <i>Mathematical Proceedings of the Cambridge Philosophical Society</i>, vol. 178, no. 3. Cambridge University Press, pp. 293–320, 2025."},"page":"293-320","language":[{"iso":"eng"}],"author":[{"full_name":"KUPERWASSER, EDEN","first_name":"EDEN","last_name":"KUPERWASSER"},{"full_name":"SAMOTIJ, WOJCIECH","last_name":"SAMOTIJ","first_name":"WOJCIECH"},{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","first_name":"Yuval","last_name":"Wigderson","full_name":"Wigderson, Yuval"}],"arxiv":1,"oa":1,"publication_identifier":{"issn":["0305-0041"],"eissn":["1469-8064"]},"scopus_import":"1","month":"04","volume":178,"title":"On the Kohayakawa–Kreuter conjecture","publication_status":"published","abstract":[{"lang":"eng","text":"Let us say that a graph G is Ramsey for a tuple (H1, ... , Hr) of graphs if every r-colouring\r\nof the edges of G contains a monochromatic copy of Hi in colour i, for some i ∈ [[r]].\r\nA famous conjecture of Kohayakawa and Kreuter, extending seminal work of Rödl and\r\nRucinski, predicts the threshold at which the binomial random graph ´ Gn,p becomes Ramsey\r\nfor (H1, ... , Hr) asymptotically almost surely.\r\nIn this paper, we resolve the Kohayakawa–Kreuter conjecture for almost all tuples of\r\ngraphs. Moreover, we reduce its validity to the truth of a certain deterministic statement,\r\nwhich is a clear necessary condition for the conjecture to hold. All of our results actually hold in greater generality, when one replaces the graphs H1, ... , Hr by finite families\r\nH1, ... , Hr. Additionally, we pose a natural (deterministic) graph-partitioning conjecture,\r\nwhich we believe to be of independent interest, and whose resolution would imply the\r\nKohayakawa–Kreuter conjecture."}],"intvolume":"       178","publication":"Mathematical Proceedings of the Cambridge Philosophical Society","OA_place":"repository","OA_type":"green","quality_controlled":"1","day":"28","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2307.16611","open_access":"1"}]}