{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:51:00Z","timestamp":1780386660030,"version":"3.54.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A weakly optimal $K_s$-free $(n,d,\\lambda)$-graph is a $d$-regular $K_s$-free graph on $n$ vertices with $d=\\Theta(n^{1-\\alpha})$ and spectral expansion $\\lambda=\\Theta(n^{1-(s-1)\\alpha})$, for some fixed $\\alpha&gt;0$. Such a graph is called optimal if additionally $\\alpha = \\frac{1}{2s-3}$. We prove that if $s_{1},\\ldots,s_{k}\\ge3$ are fixed positive integers and weakly optimal $K_{s_{i}}$-free pseudorandom graphs exist for each $1\\le i\\le k$, then the multicolor Ramsey numbers satisfy\\[\\Omega\\Big(\\frac{t^{S+1}}{\\log^{2S}t}\\Big)\\le r(s_{1},\\ldots,s_{k},t)\\le O\\Big(\\frac{t^{S+1}}{\\log^{S}t}\\Big),\\]as $t\\rightarrow\\infty$, where $S=\\sum_{i=1}^{k}(s_{i}-2)$. This generalizes previous results of Mubayi and Verstra\\\"ete, who proved the case $k=1$, and Alon and R\u00f6dl, who proved the case $s_1=\\cdots = s_k = 3$. Both previous results used the existence of optimal rather than weakly optimal $K_{s_i}$-free graphs.<\/jats:p>","DOI":"10.37236\/9071","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T10:04:47Z","timestamp":1581069887000},"source":"Crossref","is-referenced-by-count":6,"title":["Multicolor Ramsey Numbers via Pseudorandom Graphs"],"prefix":"10.37236","volume":"27","author":[{"given":"Xiaoyu","family":"He","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuval","family":"Wigderson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2020,2,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p32\/8019","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p32\/8019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T10:04:47Z","timestamp":1581069887000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/9071","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,7]]},"article-number":"P1.32"}}