{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T17:35:16Z","timestamp":1776965716467,"version":"3.51.4"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A $(p,q)$-coloring of a graph $G$ is an edge-coloring of $G$ such that every $p$-clique receives at least $q$ colors. In 1975, Erd\u0151s and Shelah introduced the\u00a0 generalized Ramsey number $f(n,p,q)$ which is the minimum number of colors needed in a $(p,q)$-coloring of $K_n$. In 1997, Erd\u0151s and Gy\u00e1rf\u00e1s showed that $f(n,p,q)$ is at most a constant times $n^{\\frac{p-2}{\\binom{p}{2} - q + 1}}$. Very recently the first author, Dudek, and English improved this bound by a factor of $\\log n^{\\frac{-1}{\\binom{p}{2} - q + 1}} $ for all $q \\le \\frac{p^2 - 26p + 55}{4}$, and they ask if this improvement could hold for a wider range of $q$.\r\nWe answer this in the affirmative for the entire non-integral regime, that is, for all integers $p, q$ with $p-2$ not divisible by $\\binom{p}{2} - q + 1$. Furthermore, we provide a simultaneous three-way generalization as follows: where $p$-clique is replaced by any fixed graph $F$ (with $|V(F)|-2$ not divisible by $|E(F)| - q + 1$); to list coloring; and to $k$-uniform hypergraphs. Our results are a new application of the Forbidden Submatching Method of the second and fourth authors.<\/jats:p>","DOI":"10.37236\/14326","type":"journal-article","created":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T16:38:41Z","timestamp":1776962321000},"source":"Crossref","is-referenced-by-count":0,"title":["On Generalized Ramsey Numbers in the Non-Integral Regime"],"prefix":"10.37236","volume":"33","author":[{"given":"Patrick","family":"Bennett","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michelle","family":"Delcourt","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lina","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luke","family":"Postle","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2026,4,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p18\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p18\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T16:38:41Z","timestamp":1776962321000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i2p18"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,24]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/14326","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,24]]},"article-number":"P2.18"}}