{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:23Z","timestamp":1753893863274,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Tur\u00e1n density $\\pi(\\cal F)$ of a family $\\cal F$ of $r$-graphs is the limit as $n\\to\\infty$ of the maximum edge density of an $\\cal F$-free $r$-graph on $n$ vertices. Erd\u0151s [Israel J. Math, 2 (1964):183\u2014190] proved that no Tur\u00e1n density can lie in the open interval $(0,r!\/r^r)$. Here we show that any other open subinterval of $[0,1]$ avoiding Tur\u00e1n densities has strictly smaller length. In particular, this implies a conjecture of Grosu [arXiv:1403.4653, 2014].<\/jats:p>","DOI":"10.37236\/5170","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:51:45Z","timestamp":1578696705000},"source":"Crossref","is-referenced-by-count":2,"title":["The Maximal Length of a Gap between $r$-Graph Tur\u00e1n Densities"],"prefix":"10.37236","volume":"22","author":[{"given":"Oleg","family":"Pikhurko","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,10,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:08:40Z","timestamp":1579255720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,30]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/5170","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,10,30]]},"article-number":"P4.15"}}