{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T20:08:14Z","timestamp":1764360494588,"version":"3.46.0"},"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>Let $ a,b \\in {\\bf Z}^+$, $r=a + b$, and let $T$ be a tree with parts $U = \\{u_1,u_2,\\dots,u_s\\}$ and $V = \\{v_1,v_2,\\dots,v_t\\}$. Let $U_1, \\dots ,U_s$ and $V_1, \\dots, V_t$ be disjoint sets, such that $|U_i|=a$ and $|V_j|=b$ for all $i,j$. The $(a,b)$-blowup of $T$ is the $r$-uniform hypergraph with edge set$ {\\{U_i \\cup V_j : u_iv_j \\in E(T)\\}.}$\r\nWe use the $\\Delta$-systems method to prove the following Tur\u00e1n-type result. Suppose $a,b,t\\in {\\bf Z}^+$, $r=a+b\\geq 3$, $a\\geq 2$, and $T$ is a fixed tree of diameter $4$ in which the degree of the center vertex is $t$. Then there exists a $C=C(r,t,T)&gt;0$ such that $ |\\mathcal{H}|\\leq (t-1){n\\choose r-1} +Cn^{r-2}$ for every $n$-vertex $r$-uniform hypergraph $\\mathcal{H}$ not containing an $(a,b)$-blowup of $T$. This is asymptotically exact when $t\\leq |V(T)|\/2$. A stability result is also presented.<\/jats:p>","DOI":"10.37236\/12197","type":"journal-article","created":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T20:05:05Z","timestamp":1764360305000},"source":"Crossref","is-referenced-by-count":0,"title":["Tur\u00e1n Number for Bushes"],"prefix":"10.37236","volume":"32","author":[{"given":"Alexandr","family":"Kostochka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zolt\u00e1n","family":"F\u00fcredi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,11,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p55\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p55\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T20:05:05Z","timestamp":1764360305000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i4p55"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,28]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12197","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,28]]},"article-number":"P4.55"}}