{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:42Z","timestamp":1753893822290,"version":"3.41.2"},"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>We consider the Tur\u00e1n problems of $2$-edge-colored graphs. A $2$-edge-colored graph $H=(V, E_r, E_b)$ is a triple consisting of the vertex set $V$, the set of red edges $E_r$ and the set of blue edges $E_b$ where $E_r$ and $E_b$ do not have to be disjoint. The Tur\u00e1n density $\\pi(H)$ of $H$ is defined to be $\\lim_{n\\to\\infty} \\max_{G_n}h_n(G_n)$, where $G_n$ is chosen among all possible $2$-edge-colored graphs on $n$ vertices containing no $H$ as a sub-graph and $h_n(G_n)=(|E_r(G)|+|E_b(G)|)\/\\binom{n}{2}$ is the formula to measure the edge density of $G_n$. We will determine the Tur\u00e1n densities of all $2$-edge-colored bipartite graphs. We also give an important application on the Tur\u00e1n problems of $\\{2, 3\\}$-hypergraphs.<\/jats:p>","DOI":"10.37236\/10068","type":"journal-article","created":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T01:34:08Z","timestamp":1631842448000},"source":"Crossref","is-referenced-by-count":0,"title":["Tur\u00e1n Density of $2$-Edge-Colored Bipartite Graphs with Application on $\\{2, 3\\}$-Hypergraphs"],"prefix":"10.37236","volume":"28","author":[{"given":"Shuliang","family":"Bai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linyuan","family":"Lu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,8,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p42\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i3p42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,17]],"date-time":"2021-09-17T01:34:09Z","timestamp":1631842449000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i3p42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,27]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,7,1]]}},"URL":"https:\/\/doi.org\/10.37236\/10068","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,8,27]]},"article-number":"P3.42"}}