{"status":"public","arxiv":1,"publisher":"The Electronic Journal of Combinatorics","OA_place":"repository","publication":"The Electronic Journal of Combinatorics","publication_identifier":{"issn":["1077-8926"]},"month":"02","intvolume":"        27","author":[{"last_name":"He","first_name":"Xiaoyu","full_name":"He, Xiaoyu"},{"id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5","last_name":"Wigderson","full_name":"Wigderson, Yuval","first_name":"Yuval"}],"external_id":{"arxiv":["1910.06287"]},"article_number":"P1.32","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2020","volume":27,"oa_version":"Preprint","date_published":"2020-02-07T00:00:00Z","article_processing_charge":"No","title":"Multicolor Ramsey numbers via pseudorandom graphs","scopus_import":"1","OA_type":"green","language":[{"iso":"eng"}],"abstract":[{"text":"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\r\nΩ(tS+1log2St)≤r(s1,…,sk,t)≤O(tS+1logSt),\r\nas 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.","lang":"eng"}],"extern":"1","quality_controlled":"1","citation":{"apa":"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>","ama":"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>","ista":"He X, Wigderson Y. 2020. Multicolor Ramsey numbers via pseudorandom graphs. The Electronic Journal of Combinatorics. 27(1), P1.32.","chicago":"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>.","short":"X. He, Y. Wigderson, The Electronic Journal of Combinatorics 27 (2020).","mla":"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>.","ieee":"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."},"date_updated":"2026-07-08T07:27:57Z","_id":"22153","issue":"1","type":"journal_article","date_created":"2026-06-29T10:47:47Z","publication_status":"published","doi":"10.37236/9071","article_type":"original","day":"07"}