{"OA_type":"green","scopus_import":"1","abstract":[{"lang":"eng","text":"Recently, Souza introduced blowup Ramsey numbers as a gener-\r\nalization of bipartite Ramsey numbers. For graphs G and H, say\r\nG r\r\n−→ H if every r-edge-coloring of G contains a monochromatic\r\ncopy of H. Let H[t] denote the t-blowup of H. Then the blowup\r\nRamsey number of G, H, r, and t is defined as the minimum n\r\nsuch that G[n] r\r\n−→ H[t]. Souza proved upper and lower bounds on\r\nn that are exponential in t, and conjectured that the exponential\r\nconstant does not depend on G. We prove that the dependence on\r\nG in the exponential constant is indeed unnecessary, but conjecture\r\nthat some dependence on G is unavoidable.\r\nAn important step in both Souza’s proof and ours is a theorem of\r\nNikiforov, which says that if a graph contains a constant fraction\r\nof the possible copies of H, then it contains a blowup of H of\r\nlogarithmic size. We also provide a new proof of this theorem with\r\na better quantitative dependence."}],"language":[{"iso":"eng"}],"oa":1,"quality_controlled":"1","citation":{"apa":"Fox, J., Luo, S., &#38; Wigderson, Y. (2021). Extremal and Ramsey results on graph blowups. <i>Journal of Combinatorics</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/joc.2021.v12.n1.a1\">https://doi.org/10.4310/joc.2021.v12.n1.a1</a>","ama":"Fox J, Luo S, Wigderson Y. Extremal and Ramsey results on graph blowups. <i>Journal of Combinatorics</i>. 2021;12(1):1-15. doi:<a href=\"https://doi.org/10.4310/joc.2021.v12.n1.a1\">10.4310/joc.2021.v12.n1.a1</a>","ista":"Fox J, Luo S, Wigderson Y. 2021. Extremal and Ramsey results on graph blowups. Journal of Combinatorics. 12(1), 1–15.","chicago":"Fox, Jacob, Sammy Luo, and Yuval Wigderson. “Extremal and Ramsey Results on Graph Blowups.” <i>Journal of Combinatorics</i>. International Press of Boston, 2021. <a href=\"https://doi.org/10.4310/joc.2021.v12.n1.a1\">https://doi.org/10.4310/joc.2021.v12.n1.a1</a>.","short":"J. Fox, S. Luo, Y. Wigderson, Journal of Combinatorics 12 (2021) 1–15.","mla":"Fox, Jacob, et al. “Extremal and Ramsey Results on Graph Blowups.” <i>Journal of Combinatorics</i>, vol. 12, no. 1, International Press of Boston, 2021, pp. 1–15, doi:<a href=\"https://doi.org/10.4310/joc.2021.v12.n1.a1\">10.4310/joc.2021.v12.n1.a1</a>.","ieee":"J. Fox, S. Luo, and Y. Wigderson, “Extremal and Ramsey results on graph blowups,” <i>Journal of Combinatorics</i>, vol. 12, no. 1. International Press of Boston, pp. 1–15, 2021."},"date_updated":"2026-07-08T10:41:31Z","extern":"1","_id":"22161","issue":"1","date_created":"2026-06-29T10:52:13Z","publication_status":"published","type":"journal_article","doi":"10.4310/joc.2021.v12.n1.a1","article_type":"original","day":"01","mathsc":["05C35","05C55"],"status":"public","arxiv":1,"publisher":"International Press of Boston","publication":"Journal of Combinatorics","OA_place":"repository","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1912.08328","open_access":"1"}],"publication_identifier":{"issn":["2156-3527"],"eissn":["2150-959X"]},"month":"01","intvolume":"        12","author":[{"first_name":"Jacob","full_name":"Fox, Jacob","last_name":"Fox"},{"full_name":"Luo, Sammy","first_name":"Sammy","last_name":"Luo"},{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","first_name":"Yuval","full_name":"Wigderson, Yuval","last_name":"Wigderson"}],"external_id":{"arxiv":["1912.08328"]},"page":"1-15","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2021-01-01T00:00:00Z","oa_version":"Preprint","volume":12,"article_processing_charge":"No","title":"Extremal and Ramsey results on graph blowups"}