{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:28Z","timestamp":1753893868520,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this paper, we consider the Tur\u00e1n problems on $\\{1,3\\}$-hypergraphs.\u00a0 We prove that a $\\{1, 3\\}$-hypergraph is degenerate if and only if it's $H^{\\{1, 3\\}}_5$-colorable, where\u00a0 $H^{\\{1, 3\\}}_5$ is a hypergraph with vertex set\u00a0 $V=[5]$ and edge set $E=\\{\\{2\\}, \\{3\\}, \\{1, 2, 4\\},\\{1, 3, 5\\}, \\{1, 4, 5\\}\\}.$ Using this result, we further prove that for any finite set $R$ of distinct positive integers, except the case $R=\\{1, 2\\}$,\u00a0 there always exist non-trivial degenerate $R$-graphs. We also compute the Tur\u00e1n densities of some small $\\{1,3\\}$-hypergraphs.\u00a0<\/jats:p>","DOI":"10.37236\/8072","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:11:36Z","timestamp":1578640296000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Tur\u00e1n Density of $\\{1, 3\\}$-Hypergraphs"],"prefix":"10.37236","volume":"26","author":[{"given":"Shuliang","family":"Bai","sequence":"first","affiliation":[]},{"given":"Linyuan","family":"Lu","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,3,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p34\/7793","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i1p34\/7793","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:16:00Z","timestamp":1579234560000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i1p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/8072","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,3,8]]},"article-number":"P1.34"}}