Bounded VC-dimension implies the Schur-Erdős conjecture Fox, Jacob Pach, János Suk, Andrew Computational Mathematics Discrete Mathematics and Combinatorics 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. Springer Nature 2021 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/15275 Fox J, Pach J, Suk A. Bounded VC-dimension implies the Schur-Erdős conjecture. <i>Combinatorica</i>. 2021;41(6):803-813. doi:<a href="https://doi.org/10.1007/s00493-021-4530-9">10.1007/s00493-021-4530-9</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00493-021-4530-9 info:eu-repo/semantics/altIdentifier/issn/0209-9683 info:eu-repo/semantics/altIdentifier/e-issn/1439-6912 info:eu-repo/semantics/altIdentifier/arxiv/1912.02342 info:eu-repo/semantics/openAccess