{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:24Z","timestamp":1753893864844,"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>Mantel's theorem says that among all triangle-free graphs of a given order the balanced complete bipartite graph is the unique graph of maximum size. We prove an analogue of this result for 3-graphs. Let $K_4^-=\\{123,124,134\\}$, $F_6=\\{123,124,345,156\\}$ and $\\mathcal{F}=\\{K_4^-,F_6\\}$: for $n\\neq 5$ the unique $\\mathcal{F}$-free 3-graph of order $n$ and maximum size is the balanced complete tripartite 3-graph $S_3(n)$ (for $n=5$ it is $C_5^{(3)}=\\{123,234,345,145,125\\}$). This extends an old result of Bollob\u00e1s that $S_3(n) $ is the unique 3-graph of\u00a0maximum size with no copy of $K_4^-=\\{123,124,134\\}$ or $F_5=\\{123,124,345\\}$.<\/jats:p>","DOI":"10.37236\/5203","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:57:46Z","timestamp":1578697066000},"source":"Crossref","is-referenced-by-count":0,"title":["An Exact Tur\u00e1n Result for Tripartite 3-Graphs"],"prefix":"10.37236","volume":"22","author":[{"given":"Adam","family":"Sanitt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Talbot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,10,16]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p3\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p3\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:08:59Z","timestamp":1579255739000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,16]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/5203","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,10,16]]},"article-number":"P4.3"}}