{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,7]],"date-time":"2026-06-07T08:50:37Z","timestamp":1780822237161,"version":"3.54.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let the crown $C_{13}$ be the linear $3$-graph on $9$ vertices $\\{a,b,c,d,e,f,g,h,i\\}$ with edges $$E = \\{\\{a,b,c\\}, \\{a, d,e\\}, \\{b, f, g\\}, \\{c, h,i\\}\\}.$$ Proving a conjecture of Gy\u00e1rf\u00e1s et. al., we show that for any crown-free linear $3$-graph $G$ on $n$ vertices, its number of edges satisfy $$\\lvert E(G) \\rvert \\leq \\frac{3(n - s)}{2}$$ where $s$ is the number of vertices in $G$ with degree at least $6$. This result, combined with previous work, essentially completes the determination of linear Tur\u00e1n number for linear $3$-graphs with at most $4$ edges.<\/jats:p>","DOI":"10.37236\/10775","type":"journal-article","created":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T07:52:05Z","timestamp":1662623525000},"source":"Crossref","is-referenced-by-count":1,"title":["On the Tur\u00e1n Number of the Linear $3$-Graph $C_{13}$"],"prefix":"10.37236","volume":"29","author":[{"given":"Chaoliang","family":"Tang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hehui","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shengtong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zeyu","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2022,8,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i3p46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,8]],"date-time":"2022-09-08T07:52:05Z","timestamp":1662623525000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i3p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,26]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/10775","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,26]]},"article-number":"P3.46"}}