{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T08:48:00Z","timestamp":1770972480504,"version":"3.50.1"},"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>Generalized Tur\u00e1n problems ask for the maximum number of copies of a graph $H$ in an $n$-vertex, $F$-free graph, denoted by $ex(n,H,F)$. We show how to extend the new, localized approach of Brada\u010d, Malec, and Tompkins to generalized Tur\u00e1n problems. We weight the copies of $H$ (typically taking $H=K_t$), instead of the edges, based on the size of the largest clique, path, or star containing the vertices of the copy of $H$, and in each case prove a tight upper bound on the sum of the weights. The generalized edge Tur\u00e1n number $mex(m,H,F)$ is the maximum number of copies of a graph $H$ in an $m$-edge, $F$-free graph. A consequence of our new localized theorems is an asymptotic determination of $ex(n,H,K_{1,r})$ for every $H$ having at least one dominating vertex and $mex(m,H,K_{1,r})$ for every $H$ having at least two dominating vertices.<\/jats:p>","DOI":"10.37236\/12132","type":"journal-article","created":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:33:45Z","timestamp":1726824825000},"source":"Crossref","is-referenced-by-count":1,"title":["A Localized Approach to Generalized Tur\u00e1n Problems"],"prefix":"10.37236","volume":"31","author":[{"given":"Rachel","family":"Kirsch","sequence":"first","affiliation":[]},{"given":"JD","family":"Nir","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2024,9,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p34\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p34\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,20]],"date-time":"2024-09-20T09:33:45Z","timestamp":1726824825000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i3p34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,20]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/12132","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,9,20]]},"article-number":"P3.34"}}