@article{15275,
  abstract     = {In 1916, Schur introduced the Ramsey number r(3; m), which is the minimum integer n > 1 such that for any m-coloring of the edges of the complete graph Kn, there is a monochromatic copy of K3. He showed that r(3; m) ≤ O(m!), and a simple construction demonstrates that r(3; m) ≥ 2Ω(m). An old conjecture of Erdős states that r(3; m) = 2Θ(m). In this note, we prove the conjecture for m-colorings with bounded VC-dimension, that is, for m-colorings with the property that the set system induced by the neighborhoods of the vertices with respect to each color class has bounded VC-dimension.},
  author       = {Fox, Jacob and Pach, János and Suk, Andrew},
  issn         = {1439-6912},
  journal      = {Combinatorica},
  keywords     = {Computational Mathematics, Discrete Mathematics and Combinatorics},
  number       = {6},
  pages        = {803--813},
  publisher    = {Springer Nature},
  title        = {{Bounded VC-dimension implies the Schur-Erdős conjecture}},
  doi          = {10.1007/s00493-021-4530-9},
  volume       = {41},
  year         = {2021},
}