@article{22161,
  abstract     = {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.},
  author       = {Fox, Jacob and Luo, Sammy and Wigderson, Yuval},
  issn         = {2150-959X},
  journal      = {Journal of Combinatorics},
  number       = {1},
  pages        = {1--15},
  publisher    = {International Press of Boston},
  title        = {{Extremal and Ramsey results on graph blowups}},
  doi          = {10.4310/joc.2021.v12.n1.a1},
  volume       = {12},
  year         = {2021},
}