article published yes Jacob Fox author Sammy Luo author Yuval Wigderson author 2d0023a0-1567-11f0-833d-d5c1e476d4b5 Recently, Souza introduced blowup Ramsey numbers as a gener- alization of bipartite Ramsey numbers. For graphs G and H, say G r −→ H if every r-edge-coloring of G contains a monochromatic copy of H. Let H[t] denote the t-blowup of H. Then the blowup Ramsey number of G, H, r, and t is defined as the minimum n such that G[n] r −→ H[t]. Souza proved upper and lower bounds on n that are exponential in t, and conjectured that the exponential constant does not depend on G. We prove that the dependence on G in the exponential constant is indeed unnecessary, but conjecture that some dependence on G is unavoidable. An important step in both Souza’s proof and ours is a theorem of Nikiforov, which says that if a graph contains a constant fraction of the possible copies of H, then it contains a blowup of H of logarithmic size. We also provide a new proof of this theorem with a better quantitative dependence. International Press of Boston2021 eng 2156-3527 2150-959X 1912.0832810.4310/joc.2021.v12.n1.a1 1211-15 yes 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> 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> Fox J, Luo S, Wigderson Y. 2021. Extremal and Ramsey results on graph blowups. Journal of Combinatorics. 12(1), 1–15. J. Fox, S. Luo, Y. Wigderson, Journal of Combinatorics 12 (2021) 1–15. 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>. 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. 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>. 221612026-06-29T10:52:13Z2026-07-08T10:41:31Z