{"doi":"10.1007/s00493-021-4409-9","month":"06","scopus_import":"1","extern":"1","language":[{"iso":"eng"}],"article_type":"original","volume":42,"date_published":"2022-06-01T00:00:00Z","title":"Ramsey numbers of books and quasirandomness","year":"2022","date_updated":"2026-07-14T08:57:12Z","publication_identifier":{"eissn":["1439-6912"],"issn":["0209-9683"]},"arxiv":1,"type":"journal_article","abstract":[{"lang":"eng","text":"The book graph B\r\n(k)\r\nn consists of n copies of Kk+1 joined along a common Kk. The Ramsey\r\nnumbers of B\r\n(k)\r\nn are known to have strong connections to the classical Ramsey numbers\r\nof cliques. Recently, the first author determined the asymptotic order of these Ramsey\r\nnumbers for fixed k, thus answering an old question of Erd˝os, Faudree, Rousseau, and\r\nSchelp. In this paper, we first provide a simpler proof of this theorem. Next, answering a\r\nquestion of the first author, we present a different proof that avoids the use of Szemer´edi’s\r\nregularity lemma, thus providing much tighter control on the error term. Finally, we prove\r\na conjecture of Nikiforov, Rousseau, and Schelp by showing that all extremal colorings for\r\nthis Ramsey problem are quasirandom"}],"citation":{"apa":"Conlon, D., Fox, J., &#38; Wigderson, Y. (2022). Ramsey numbers of books and quasirandomness. <i>Combinatorica</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00493-021-4409-9\">https://doi.org/10.1007/s00493-021-4409-9</a>","ama":"Conlon D, Fox J, Wigderson Y. Ramsey numbers of books and quasirandomness. <i>Combinatorica</i>. 2022;42(3):309-363. doi:<a href=\"https://doi.org/10.1007/s00493-021-4409-9\">10.1007/s00493-021-4409-9</a>","ista":"Conlon D, Fox J, Wigderson Y. 2022. Ramsey numbers of books and quasirandomness. Combinatorica. 42(3), 309–363.","chicago":"Conlon, David, Jacob Fox, and Yuval Wigderson. “Ramsey Numbers of Books and Quasirandomness.” <i>Combinatorica</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00493-021-4409-9\">https://doi.org/10.1007/s00493-021-4409-9</a>.","ieee":"D. Conlon, J. Fox, and Y. Wigderson, “Ramsey numbers of books and quasirandomness,” <i>Combinatorica</i>, vol. 42, no. 3. Springer Nature, pp. 309–363, 2022.","mla":"Conlon, David, et al. “Ramsey Numbers of Books and Quasirandomness.” <i>Combinatorica</i>, vol. 42, no. 3, Springer Nature, 2022, pp. 309–63, doi:<a href=\"https://doi.org/10.1007/s00493-021-4409-9\">10.1007/s00493-021-4409-9</a>.","short":"D. Conlon, J. Fox, Y. Wigderson, Combinatorica 42 (2022) 309–363."},"oa_version":"Preprint","author":[{"full_name":"Conlon, David","first_name":"David","last_name":"Conlon"},{"full_name":"Fox, Jacob","last_name":"Fox","first_name":"Jacob"},{"last_name":"Wigderson","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","full_name":"Wigderson, Yuval"}],"OA_type":"green","_id":"22174","article_processing_charge":"No","quality_controlled":"1","external_id":{"arxiv":["2001.00407"]},"publication":"Combinatorica","status":"public","OA_place":"repository","oa":1,"publisher":"Springer Nature","page":"309-363","intvolume":"        42","publication_status":"published","day":"01","date_created":"2026-06-29T10:57:27Z","issue":"3","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2001.00407"}]}