{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T21:13:07Z","timestamp":1779397987765,"version":"3.53.1"},"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>What is the least integer $\\text{sd}(n)$ such that every graph on $n$ vertices has fractional chromatic number $p \/q$, where $p$ and $q$ are positive integers and $q \\le \\text{sd}(n)$? An upper bound on the determinants of Hadamard matrices implies that $\\text{sd}(n)\\le 2^{-n}(n+1)^{(n+1) \/2}$. The only known lower bound on $\\text{sd}(n)$ that is exponential in $n$ (asymptotically, roughly $1.346^n\/\\sqrt{\\log n}$) was obtained using an iterated Mycielski construction [D. C. Fisher, J. Graph Theory 20 (1995), 403-409]. We improve on this bound by constructing a family of graphs which shows that $\\text{sd}(n) \\geq 2^{n\/2}$.<\/jats:p>","DOI":"10.37236\/14524","type":"journal-article","created":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T20:51:24Z","timestamp":1779396684000},"source":"Crossref","is-referenced-by-count":0,"title":["Lower Bound on the Maximum Denominator of Fractional Chromatic Numbers"],"prefix":"10.37236","volume":"33","author":[{"given":"Marthe","family":"Bonamy","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Karol\u00edna","family":"Hylasov\u00e1","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tom\u00e1\u0161","family":"Kaiser","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-S\u00e9bastien","family":"Sereni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2026,5,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T20:51:24Z","timestamp":1779396684000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i2p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/14524","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,22]]},"article-number":"P2.38"}}