article published yes Xiaoyu He author Yuval Wigderson author 2d0023a0-1567-11f0-833d-d5c1e476d4b5 A weakly optimal Ks-free (n,d,λ)-graph is a d-regular Ks-free graph on n vertices with d=Θ(n1−α) and spectral expansion λ=Θ(n1−(s−1)α), for some fixed α>0. Such a graph is called optimal if additionally α=12s−3. We prove that if s1,…,sk≥3 are fixed positive integers and weakly optimal Ksi-free pseudorandom graphs exist for each 1≤i≤k, then the multicolor Ramsey numbers satisfy Ω(tS+1log2St)≤r(s1,…,sk,t)≤O(tS+1logSt), as t→∞, where S=∑ki=1(si−2). This generalizes previous results of Mubayi and Verstraëte, who proved the case k=1, and Alon and Rödl, who proved the case s1=⋯=sk=3. Both previous results used the existence of optimal rather than weakly optimal Ksi-free graphs. The Electronic Journal of Combinatorics2020 eng 1077-8926 1910.0628710.37236/9071 271 yes He, Xiaoyu, and Yuval Wigderson. “Multicolor Ramsey Numbers via Pseudorandom Graphs.” <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics, 2020. <a href="https://doi.org/10.37236/9071">https://doi.org/10.37236/9071</a>. X. He, Y. Wigderson, The Electronic Journal of Combinatorics 27 (2020). He, Xiaoyu, and Yuval Wigderson. “Multicolor Ramsey Numbers via Pseudorandom Graphs.” <i>The Electronic Journal of Combinatorics</i>, vol. 27, no. 1, P1.32, The Electronic Journal of Combinatorics, 2020, doi:<a href="https://doi.org/10.37236/9071">10.37236/9071</a>. X. He and Y. Wigderson, “Multicolor Ramsey numbers via pseudorandom graphs,” <i>The Electronic Journal of Combinatorics</i>, vol. 27, no. 1. The Electronic Journal of Combinatorics, 2020. He, X., &#38; Wigderson, Y. (2020). Multicolor Ramsey numbers via pseudorandom graphs. <i>The Electronic Journal of Combinatorics</i>. The Electronic Journal of Combinatorics. <a href="https://doi.org/10.37236/9071">https://doi.org/10.37236/9071</a> He X, Wigderson Y. Multicolor Ramsey numbers via pseudorandom graphs. <i>The Electronic Journal of Combinatorics</i>. 2020;27(1). doi:<a href="https://doi.org/10.37236/9071">10.37236/9071</a> He X, Wigderson Y. 2020. Multicolor Ramsey numbers via pseudorandom graphs. The Electronic Journal of Combinatorics. 27(1), P1.32. 221532026-06-29T10:47:47Z2026-07-08T07:27:57Z